They have interest in character building, or narrative building, which is why they push back when their tools are restricted.
Some players likely do care, but looking at r/LFG and my own experience, I don’t think players reliably self-select away from games with restrictions. That makes it hard for me to see this as a dominant concern for most players.
If anything, D&D Beyond data suggests most characters cluster around a small number of races, which suggests that broad racial availability may not be a priority for many. In practice, players also seem to react much more strongly to class restrictions than racial ones. In my own r/LFG posts, restricting classes produces a noticeable drop in responses, while restricting races doesn’t.
Honestly, I’m increasingly thinking about restricting races as a way to filter out players who expect every official option to be available. In my experience, that expectation often correlates with friction in other areas, such as: magic item availability, objections to house rules, resistance to limits on spells like silvery barbs or counterspell, and sometimes push back against homebrew monsters. All of which, simply aren't worth my limited free time to resolve.
Maybe I’m wrong, but this thread has made me more pro-restriction. I don’t expect to have trouble finding players either way, and this helps filter out table dynamics I don't enjoy. I value players who are aligned from the start, not ones who want to debate every deviation from the baseline rules.
But I'm sure this will be an unpopular opinion around here.