The center tap on the 5VAC winding helps to balance the ripple pulses from the rectifier. If you take the B+ from one side of the rectifier (either pin 2 or 8) and look at the unfiltered pulses you will see that every other pulse will be slightly bigger. This will have the effect of putting a small 60Hz fluctuation on top of the unfiltered pulses, so you will have a big 120Hz ripple component and a tiny 60Hz component as well. Don't mean too much in a lo-fi guitar amp but might be worth a dime in a hi-fi amp.
If I had a center tap I would use it, if only for bragging rights, "Mine's smoother than yours". The center taps works the same for all those 5V rectifier tubes...
I think it will work like that for direct / heater cathode types, eg 5Y3 / 5U4, but not for indirectly heated cathodes such as the GZ34 in the post #1 schematic.
Marshall made the mistake of taking the HT output from pin 2 when they designed/built the 90s AC30TBX for Korg Vox. The combination of their stupid hot switching standby and passing the HT current via the heater filament tended to result in a blown heater for the GZ34.
With the HT output (and hence reservoir cap) correctly wired to pin 8, the 5V heater signal at pin 2 is forced to swing above and below the Vac reference at pin 8. ie it doesn’t add any ripple to the HT.
Taking to HT from a 5V winding CT wouldn't be a good move, as it would force some HT current to flow via the filament (which as Marshall proved can shorten heater life) and it would add a portion of the 5V on to the HT output, which wouldn't be there if taken from pin 8. I can't see whether it would be 2.5V or 1.25V, so a negligible amount but whatever, it's a retrograde change.