A kung fu fighter in a disco

I don't think the recessive vocal really is "doing the best [one] can with the voice [one] has" -- there isn't really a correlation between how good your voice is, how well you can hold a tune, and how much expression you can put into your singing. The problem is that it sounds embarrassing in your own ears. I'm fairly confident that everyone, even the tone deaf, can do a passable parody of, say, the balladeer over-emotive style: but it generally sounds silly, and sounds especially silly from an untrained or weak voice. Theoretically, there's an in-between stage where the voice sounds expressive and not stupid, but it's hard work finding it, and people very often assume that singing with emotion automatically means sounding stupid.

So I don't think it's people accepting their limitations, I think it's people intentionally limiting themselves to a lowest-common-denominator singing style, which is socially the most accepted style for someone with a weak voice, or an untrained voice, or a strong voice that's shy.