I'd actually suggest putting this up for a vote just to see how hackish/partisan republicans really are. Could be a tough vote for some of the members
Same. Put them on record. I want to see who wouldn't vote to impeach trump over sending a terrorist mob to kill the VP and Congressmen, but who will vote to impeach Biden over nothing.
I hate to say it, but this is an easy out for all too many Republican Congress members. Very very few I believe would be threaten to buy a serious primary challenge over this, or otherwise be among the crazy caucus like MTG, Jordan, Etc.
Instead, it gives them a total straw man to knock down and then trumpet about how bipartisan and reasonable they are for not supporting a resolution stemming from literal mental illness. It effectively give them cover as being so-called middle of the road and reasonable despite voting against impeachment today on the flimsiest of pretexts.
You are probably right that there are a handful of them who could (and would) do that, but I would bet the majority of the R caucus would vote to impeach Biden on day 1 if it were put to a vote. This shouldn't be surprising, because a majority of them just voted in opposition to Biden becoming President in the first place despite the fact that he won the election, with the only reason they voted against this being lunatic conspiracy theories.
So I think you are giving the vast majority of House Republicans way too much credit.