While it's true NFL head coaching jobs are scarce and openings even more scarce, it's also true great NFL head coaches are scarcer yet.
So, the Rams are in competition for the best available and the best available very well could find the Rams personnel at a couple critical positions to be enough of a concern to sway them toward the competition.
But the real problem with all of this, of course, is that the focus remains on the next head coach rather than the next person who should be choosing the head coach. Given that, we're just relying on people who don't know what they're doing getting lucky again, so the head coaching search for the Rams is just a glorified crap-shoot. Chances are just as good that their 3rd or 4th choices will end up as good as their top two choices. None of this other stuff really matters, unfortunately. Just let em' roll and hope for the best.