How important is a Linear Power Supply Versus a Switcyed one?

The amplifiers I use to drive subwoofers are AB and have switching supplies. No transformers. They certainly have no trouble providing a lot of current on demand. For a Phono amp I don't see why not as long as it was well filtered. I'm not sure way the sound would change. If both supplies were well designed it shouldn't. The advantage of the switching supply is efficiency. Maybe it would be a good idea if you run your house on solar panels. 

They say that SMPs introduce noise into the circuit that could impact the sound quality. Sutherland says it's better to have an LPS, but he wasn't acting like it was a really big deal, claims he doesn't like to make minor changes to his personal system but would tell a family member to do it if asked.

I agree with some of the other posts that it would depend on the system as to whether or not I would hear it, and unfortunately, a trial wouldn't be feasible. 

If it was only one or two hundred bucks, I would just do it because it can't hurt (like when I bought better power cables and didn't hear a difference) and I wouldn't be upset about it, but $400 is something more considerable. I guess it all depends on your mentality on spending.

Oh well, I'll think about it....there are certainly bigger issues in the world....maybe if I can get someone reliable to do the install and drop it to $350 and not have to ship the whole unit....

Any power supply introduces noise.  Linear PS is also switching (at max voltage).  The question is how much noise?  They had to have a reason to implement SMPS.  Switchers are usually used for their efficiency when high currents are required or for size when Linear PS takes too much space (wall-warts).  It is neither case so I thought there was a third reason - they can be designed to be extremely quiet, much quieter than Linear PS.  Otherwise why do it?  It is more expensive and more complicated than Linear PS, that has just few very cheap components.   There must be a reason.  Phono stage has RIAA correction that amplifies low frequencies.  It is +20dB@20Hz and likely +12dB@120Hz.  It is likely that it is also sensitive to low frequency power supply noise (120Hz) - common for Linear PS.

Kijank-if SMPS is more expensive, then why is it standard and LPS an extra cost option?

I don't know.  Perhaps SMPS is in standard production while LPS is not (requires modifications).