There are a very small handful of people online (fewer than 5) who fret endlessly about step response and drone on and on about how the power supply needs to be rock solid when simulated.
The natural solution to satisfying these simulations would be to shunt regulate the high voltage power supply, but this particular group of people will denounce that for a variety of unspecific reasons. While they will use step response to justify how "good sounding" their amplifiers are, they are somehow also able to denounce an amplifier with perfect step response as being flawed. A shunt regulator would have no step provided the regulator shunted more current than the step, which is not at all hard to do.
This same group of people also tend to suggest much lower operating current than the book values for "long life" of output tubes, but they don't adjust the output transformer primary impedance. This will create a large difference between the quiescent plate current and the average plate current, which will either require a stiffly regulated power supply or a power supply that would otherwise be designed for a class AB push-pull amp. This also decreases output power substantially and nudges up THD.
None of this has had any influence over our kit designs. We find the low DCR power transformers espoused to be rather magnetically noisy, we design our output stages to avoid the step in the first place, and we pay attention to properly driving output stage Miller capacitance.
If this path of DIY interests you, you should certainly not let me stop you from pursuing it.
(You are also correct that the power supply requirements for a phono preamp are significantly different than those for a power amp.)