Speaking to the original poster's question . . . yes, there are side effects to unduly increasing the filter capacitance, even though there are many "high end" amplifiers that are designed without regard to them.
Keeping focused on conventional solid-state amps like your Hafler . . . these are indeed simple unregulated supplies, and (ignoring startup conditions) the main filter capacitors have three functions: the first and most obvious, is to smooth AC ripple voltage on the supply rails. The basic equations for this aspect of their design are of course widely documented.
The second role (and what most of the discussion seems to be about) is to dampen short-term changes in supply voltage, as caused by variations in amplifier current draw with the level of the music, and periodic fluctuation of the mains voltage. The key word here is "dampen", because when combined with the losses upstream of the capacitors (mainly the transformer), a resonant circuit can form with a peaked response, causing such variations to get larger.
The only way to avoid this situation is to model the transformer losses with reasonable accuracy, and calculate or simulate the power-supply response to very low frequencies . . . as it is very difficult to sweep an amplifier with a stimulus through the milli-Hertz region and measure the power-supply's reaction. Atmasphere mentions the possibility of motorboating, and this is indeed a concern with piling on the capacitance on a traditional C-L-C-filtered tube amp. But it's not nearly as much of an issue on your Hafler, as it affects both the positive and negative rails symmetrically (common-mode), to which most solid-state amps have excellent very-low-frequency noise rejection. Also, the capacitors are effectively acting in series, so the change in capacitance is somewhat less than it seems like it "should" be when you're dealing with the volumetric constraints of squeezing bigger cans in an existing chassis.
But the third role of the main filter capacitors is what's usually overlooked: they are in series with the output ground, and return the speaker current back to the supply. This is true even in a fully DC-coupled amplifier - although it may appear that the transformer center-tap is the supply return, in practice the transition from the filter caps to the center-tap occurs at a frequency several octaves below the audioband. Indeed, many "DC coupled" amplifiers will operate quite happily with their center-tap disconnected, so long as there's something in place to keep them from actually having to amplify anything approaching DC.
So what does this mean? Electrolytics of course have well-documented distortion mechanisms as they approach low-frequency rolloff, but since they're very effectively enclosed within the global feedback loop (at the frequencies where feedback is highest) this is unlikely to manifest itself in the output to virtually any degree. But they also have significant inductance, which has the effect of reducing the effectiveness of global feedback as frequency increases. Put another way . . . as frequency rises the main filter caps get lossier, thus a signal voltage starts to appear across them . . . and the amount of error that the feedback must compensate for increases.
This can be especially injurious as the amount of available global feedback is also usually falling at 6dB/octave as frequency increases, due to the amplifier's frequency compensation scheme. If the amplifier is operating in class B (including the class B region of a "class AB" amplifier) the speaker current manifests itself as a pair of half-waves (i.e. the voice of a DALEK) across each respective filter capacitor. And while these half-waves are symmetrical and supposed to cancel each other out, big electrolytics have the widest tolerances of any electrical component . . . so they won't be matched anything close to perfectly . . . the remaining difference is one more little mess that increases as the amount of global feedback to clean it up decreases.
So getting back around to increasing filter capacitance . . . the other thing that comes with increased capacitance is increased inductance. My question would be instead: if there's room and budget and the capacitance is already more than sufficient . . . why not increase the voltage rating, to improve the longevity, ESR, and inductance characteristics instead? A good designer chooses these components just like they should choose all the others . . . by finding the BEST ones to perform all aspects of their role in the circuit - not simply by grabbing the biggest/fanciest/prettiest/costliest thing they see, and sticking it in place.
Keeping focused on conventional solid-state amps like your Hafler . . . these are indeed simple unregulated supplies, and (ignoring startup conditions) the main filter capacitors have three functions: the first and most obvious, is to smooth AC ripple voltage on the supply rails. The basic equations for this aspect of their design are of course widely documented.
The second role (and what most of the discussion seems to be about) is to dampen short-term changes in supply voltage, as caused by variations in amplifier current draw with the level of the music, and periodic fluctuation of the mains voltage. The key word here is "dampen", because when combined with the losses upstream of the capacitors (mainly the transformer), a resonant circuit can form with a peaked response, causing such variations to get larger.
The only way to avoid this situation is to model the transformer losses with reasonable accuracy, and calculate or simulate the power-supply response to very low frequencies . . . as it is very difficult to sweep an amplifier with a stimulus through the milli-Hertz region and measure the power-supply's reaction. Atmasphere mentions the possibility of motorboating, and this is indeed a concern with piling on the capacitance on a traditional C-L-C-filtered tube amp. But it's not nearly as much of an issue on your Hafler, as it affects both the positive and negative rails symmetrically (common-mode), to which most solid-state amps have excellent very-low-frequency noise rejection. Also, the capacitors are effectively acting in series, so the change in capacitance is somewhat less than it seems like it "should" be when you're dealing with the volumetric constraints of squeezing bigger cans in an existing chassis.
But the third role of the main filter capacitors is what's usually overlooked: they are in series with the output ground, and return the speaker current back to the supply. This is true even in a fully DC-coupled amplifier - although it may appear that the transformer center-tap is the supply return, in practice the transition from the filter caps to the center-tap occurs at a frequency several octaves below the audioband. Indeed, many "DC coupled" amplifiers will operate quite happily with their center-tap disconnected, so long as there's something in place to keep them from actually having to amplify anything approaching DC.
So what does this mean? Electrolytics of course have well-documented distortion mechanisms as they approach low-frequency rolloff, but since they're very effectively enclosed within the global feedback loop (at the frequencies where feedback is highest) this is unlikely to manifest itself in the output to virtually any degree. But they also have significant inductance, which has the effect of reducing the effectiveness of global feedback as frequency increases. Put another way . . . as frequency rises the main filter caps get lossier, thus a signal voltage starts to appear across them . . . and the amount of error that the feedback must compensate for increases.
This can be especially injurious as the amount of available global feedback is also usually falling at 6dB/octave as frequency increases, due to the amplifier's frequency compensation scheme. If the amplifier is operating in class B (including the class B region of a "class AB" amplifier) the speaker current manifests itself as a pair of half-waves (i.e. the voice of a DALEK) across each respective filter capacitor. And while these half-waves are symmetrical and supposed to cancel each other out, big electrolytics have the widest tolerances of any electrical component . . . so they won't be matched anything close to perfectly . . . the remaining difference is one more little mess that increases as the amount of global feedback to clean it up decreases.
So getting back around to increasing filter capacitance . . . the other thing that comes with increased capacitance is increased inductance. My question would be instead: if there's room and budget and the capacitance is already more than sufficient . . . why not increase the voltage rating, to improve the longevity, ESR, and inductance characteristics instead? A good designer chooses these components just like they should choose all the others . . . by finding the BEST ones to perform all aspects of their role in the circuit - not simply by grabbing the biggest/fanciest/prettiest/costliest thing they see, and sticking it in place.