... *why* do the filaments need to be grounded?
They don't.
But the insulation inside the valve between the cathode and the heater inside it is only rated up to 100V, sometimes 200V.
If it fails, hum and buzz from the heater piwer will contaminate the signal path, and if it's a hard short, valve operation may be affected.
So, the heater and cathode circuits both need a path reference to the same point, so that the voltage between them can't drift too far apart.
Circuit common 0V / ground is a convenient point that meets that requirement, so is often used.
Another requirement is that the heater circuit has a low impedance path to circuit common. If it doesn't, it will pick up spurious ghost voltage from magnetic fields in the local area (eg mains transformer, output transformer, choke).
That spurious voltage can't deliver current, doesn't affect the voltage applied to the valve heaters, but it will tend to cause interference / noise / oscillation.
So either a direct connection to common, or a reasonably high value capacitor between the heater circuit and common, is needed.
It would be really beneficial for you to read and get your head around
http://www.valvewizard.co.uk/heater.htmlIf you have any queries, ask!
