Instead, conservatives focus on the ID mandate, ahead of fixing the inherent supply issues. Indeed, while I still have objections after this issue is fixed, they're largely irrelevant to the political mainstream.
Generally I'm opposed to anything that smacks of 'papers place', and the government has a higher bar to need to confirm and record identity than John Q. Public (also I'd note, the examples you cited, generally do not record anything, they just verify age of purchaser).
It all boils down to some form of absurd partisanship.
Or imagine if you saw Democrats proposing this?
The things that they do nothing on are "wedge" issues. The filibuster guarantees that those are the only things that can't get passed if Congress stays vaguely equally divided. Passing material improvements to average lives is no benefit to either side.
Driving requires a specific credential and is not relevant for this discussion.
Flying is another case, you do not need an ID to fly, there are provisions to fly without photo ID if you do not have one, they're just more time consuming and meant to be somewhat punitive.