how does current work in an amplifier?

So.....all other things being equal (same room, same source, same cables, same other characteristics of the amplifier), am I to understand that an amp that delivers more current would do a better job of driving a 4 ohm speaker, like Magnepan MG12's, than would an amp with less current?

Actually, as 4 ohm speakers go, I think Magnepans are less current hungry than many. They do like lots of power though.

It just depends on the amp-speaker combination and how high a listening level you prefer. Once the power supply of the amplifier is maxed out, the output signal voltage is not going to be able to match the input signal waveform, ie. distortion. The bass requires the most power, so it is the bass that starts to sound flabby or weak. At least, that is my experience...

The KISS answer to your second question is YES. An amplifier rated for a continuous 4 ohm load should handle 4 ohm nominal speakers better than an amplifier that is only rated for a continuous 6 ohm load. You're probably safe to make comparisons within a brand, but I don't think advertised specs really mean much when comparing different brands.

Looking at the question from an 'ohms law' perspective, it is a red herring question.
Even my (alleged) current hungry Magnepans have only a 4 amp fuse on the mid / tweets. Say the low is good for 6 amps.....so the speaker can take a total of 10 amps.
I2R=watts.....so 10*10*5=500 watts at about 5 ohms. That's about it.
Well, the other way to go about it is to MEASURE your speaker. I stuck a DVM on my panels......About 8vac was about the highest value I saw flicker by. Say I double that to 16vac. Since Watts=E2/R That gives me just over 50 watts.
I'll give everyone the benefit of the doubt and double that twice for 200 watts per channel into my panels.
That, sir, is loud....no LOUDER
That is why my opinion, strongly held is that amp amps while not meaningless sure depend on the ability of it to drive those amps at a reasonable voltage to provide POWER.

Don't forget the SOR of a semiconductor. Safe Operating Range. You'd need a real bunch of 'em to sustain 50 amps at 50 volts..........=2500 watts.