external power supplies

In preamps, do external power supplies make a real or theoretical improvement? (less noise)
Long ago when tube preamp circuits were very prone to hum pickup it was a good idea to keep the power supply physically separated from the amplification circuits. In power amps too!.

But it all depends on the circuitry. I built a Heathkit preamp that had lots of shielded wires, some of them further enclosed in a spring-like sheath. It hummed. Later I built a dynakit preamp which not only had no shielded wire, but didn't even have twisted pairs. It was dead quiet. Same tube types, but different circuitry.

Having the power supply on a separate chassis permits the preamp to be smaller and cosmetically attractive. It is not necessary for performance reasons.
External supplies can be bot good and bad. Good in that you put some distance between the power magnetics and amplifier circuitry. Bad because it costs more, adds extra cabling and possible ground loops.

I have a Tom Evans Vibe pre-amp. The fisrt version had a wall wart type power supply. Next came the Pulse power supply consisting of two box external power supply. I am expecting the next generation any day, the Pulse 2, with a single large external power supply. Each step has yielded massive upgrade to the sound floor. I expect the Pulse 2 to again go way beyond the previous version. I cannot comment on the single box vs two box approach. I can however confirm the importance of intelligent power supply in this hobby. For the sake of disclosure, I am also heavily invested in Isoclean equipment.
I believe it is a theoretical advantage on today's line stages. Back in the days of real preamps (with built in phono stages), a seperate supply had real value. The smaller the signal, the more it needed to be sheilded from magnetic interfence from the power supply.

As of today, when most 'preamps' are actually line stages, the signal is strong enough, and the power supplies can be internally shielded well enough, that seperate power supplies really are only theoretical improvements.

I guess if you are still considering a full function preamp (w/phono) today, there could possibly be a slight audible difference from the phono source with an internal vs. external supply.

Post removed 
Well, in theory.........you could introduce some RF noise and other crud along the cable from the supply to the preamp. Keeping the power transformers as far away as possible from sensitive circuitry is a good idea.

(Also applies to amps like the S-150. Hope Nelson isn't reading this. Inside joke.)
I've wondered why there are no amps with external power supplies. Espescially class A, where the heat can get to the caps. There were the Rowland batteries back in the day and the Coda System 100 that seperated the input section. Joule has it's variac. Almost forgot about that Mission/Cyrus optional PS.

Is it just a matter of packaging and financial restraints or is it market and tradition driven, expecting big boxes? Considering the weight and size of some the big amps, perhaps they would be better off in 2 chasis. It could also lead to a modular design and vertical upgrade path.

A while back, I came across some foot square by 4" heat sinks and I seriously considered building some DIY amps with external power supplies and EI trannys. The amplifier boxes would have been one foot cubes, two-thirds of which would have been aluminum fins. Of course, what stopped me is that I have no idea of what I'm doing.