About the only reason to go with green (or blue) would be if the background will be getting populated with OTHER assets in addition to the white.
If you will be cross-fading from some “real world” location to the white room for example, or adding something like the “weapons racks” from Matrix.
If you’re truely only going to have pure white in these shots … yeah, just shoot on white!
Well ….. I suppose there’s one other practical reason to shoot on green….
If the cyc is already green and you’ll need to paint the whole thing white, then green again after the shoot, for just a couple shots and budget/time won’t allow for that. :p
Have fun.