Why does an ADIRU 1 failure disable all functions of the A330/340’s GPWS - even those not requiring ADIRU data?
You wrote:


  (...) the GPWS's original functions (...) require only radioaltimeter data (...)


That's wrong. The basic GPWS needs barometric data alongside the RA.$^{[1][2]}$ (Not talking enhanced functions of EGPWS here, rather the most basic modes 1–3, and mode 4 needs airspeed/Mach with RA.)

The A340's GPWS computer (EGPWC) takes this barometric info (vertical speed) from ADIRS 1 (schematic), if that's failed, so would the basic GPWS.



$^1$: GPWS patent from 1970
$^2$: Aircraft Instrumentation and Systems (page 342 snippet below)


  


Note: Computing the height time derivative ($\dot h$) is not as easy as using V/S, you need high sampling rate and a perfect radar lock that won't be fooled by say trees or uneven ground reflecting the signal away. In France, some airports use radar reflectors on masts to fool the RA into thinking the ground is flat:


  
  Source: lustublog.com (in French)