Does a DAC need a large/strong power supply?

Yes and no, the power supply on the cheaper streamers do introduce noise into the system.  Like with the blusound node.  It's a great streamer but getting a better quality power cable does help out a lot.  I've also heard one modded to use an external power supply and it does help out a lot.  But with any decent built >$1000 DAC, you wont have an issue with that.

Many hifi designers believe you are essentially listening to a power supply that is merely controlled and regulated by your pre and power amps?

Some people want their DAC to sound like nothing, similar to how some people believe that the best preamp is just a passive one with a quality attenuator - nothing but a straight line with gain

This is largely a problem if one like listening to their music at very low levels.
In that case the output impedance of the passive passive pre amp screams towards infinity… and any low impedance power amp, and the capacitance or inductance in interconnects, then becomes a real (filter) effect to consider.

Many hifi designers believe you are essentially listening to a power supply that is merely controlled and regulated by your pre and power amps?

And this is also largely true.
The stiffer, and lower noise of the power supply is what does separate the men from the boys in the better sounding gear.

But, answer the OP’s question, it also makes a difference as to what the input impedance of the preamp is, and what the output impedance of the DAC is.
It the pre amp has a 1000 ohm input impedance versus, say a 100k ohm input impedance, then a 600 ohm output impedance will likely be dragged down more.

The Audio Precision measurement gear likely has a super high input impedance, so it does not likely suffer… or it is not likely to pull down the DAC’s output in any measurable way whatsoever.

Luckily, most manufacturers provide the input and output impedances of their gear. So that helps to a large degree.

Tony,

It was an honest question. I am very confused by ASR loving these cheap DACs. My Yiggy has a very large PS and sounds great. My interest is curiosity as to how these $300 to $600 dacs test so well and have very low noise. I believe they have small power supplies due to the tiny sizes of these units. I don't have an "ASR Bias", just wondering if we're all paying too much.

The BRYSTON BDA-3 DAC has independent power supplies, a feature representative in high-end DAC design, and resulting stepped-up audio performance in high-end DACs.