GNSS may be used in lieu of DME in all instrument procedures. When using GNSS in lieu of DME on an ILS procedure, care must be taken to ensure that the correct reference waypoint is used
There is a small problem with your theory. Where there are 2 ILS approaches available, one will be referenced off a VOR/DME and the other will be referenced off the ILS/DME. Only the plate referencing the VOR/DME will allow GPS in leiu of DME. The other plate does not allow it. The reason is that DME's are not stored in navigation databases as a stand alone point.
The reference waypoint for any NDB/DME or VOR/DME is the location of the NDB or VOR respectively. They are deemed to be co-located and the difference in physical location is small enough not to cause a problem.
The reference location for any ILS installation is the localizer antenna array. This could be several hundred metres from the DME and as such GPS in leiu of DME is not allowed.
The safety implication for using the wrong reference on an ILS is... a 'failed' GS integrity check and a missed approach. You'd do it once, learn from the error and not do it again.
The saftey implications of using the wrong reference on an ILS are fairly significant I would have thought...in the case of YSSY ILS 34L the reference point giving you distance would be some 2000m from your intended touchdown point....the figures would be way out. Are you going to trust the GS, or the GPS distance numbers, which won't match those on the plate?