Why does an ADIRU 1 failure disable all functions of the A330/340’s GPWS - even those not requiring ADIRU data? Among the many (many many) aircraft systems degraded or rendered unavailable to the flightcrew of QF72 as a result of a partial intermittent ADIRU 1 (Air Data / Inertial Reference Unit 1) failure, the aircraft’s GPWS was rendered totally inoperative (all emphasis mine):

0440 [. . . . .] NAV GPWS FAULT [. . . . .] The GPWS required ADIRU parameters such as true track angle, computed airspeed, true airspeed and roll attitude, and it was only connected to ADIRU 1. A problem with ADIRU 1 resulted in a loss of the GPWS function.  [ATSB Transport Safety Report AO-2008-070, page 48 (page 68 of the PDF file of the report).]
In addition to the potential for a pitch-down command, other known effects associated with the data-spike failure mode on the A330/A340 included:
[...]

unavailability of some other aircraft systems, depending on the ADIRU involved. For example, in cases where ADIRU 1 was affected, the ground proximity warning system (GPWS) was no longer available.  [Page 200/220.]


It makes sense that those GPWS functions requiring ADIRU input would be rendered inoperative by a loss of ADR/IR data;1 for instance, excessive-descent-rate protection and terrain-ahead avoidance both require pressure altitude (to calculate the aircraft’s descent rate, in the former’s case, and to determine whether the aircraft has enough altitude to safely clear rising terrain ahead, for the latter), an ADR parameter, while bank-angle protection requires roll attitude, an IR parameter.
However, not all GPWS functions require ADR or IR input; for instance, of the GPWS’s original functions, most (dangerously low height above terrain when not configured for landing; excessive terrain-closure rate; loss of height after takeoff) require only radioaltimeter data2 (plus, for the first, aircraft-configuration data), which is unaffected by even a complete loss of all air and inertial data.
So why does a loss of air-data and inertial inputs disable even the functions of the A330/340’s GPWS not requiring said inputs?

1: Although this raises the obvious question as to why such a safety-critical system as the GPWS was connected to only a single ADIRU, with no ability to switch its inputs to a different source should ADIRU 1 fail.
2: The very factor that makes the radioaltimeter inferior to the baroaltimeter for most purposes (its measuring height above the variably-high ground, rather than altitude above mean sea level) makes it ideally-suited for the GPWS basic functions (as we are interested in not colliding with the ground, rather than with mean sea level; indeed, in some cases, the ground is located below mean sea level).
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)