The studio I used to work at was one of the first ADAT studios back in the 90s, and they did a lot of rock. One of the ways they got past the limitations of the medium was to compress and limit to tape. You generally don't want to do that unless you have tons of time to set up and get it right (a la Rudy Van Gelder), which was not in most budgets. But it worked well enough and the ADAT recordings out of this studio sounded way better than most.
Mercifully storage has gotten cheaper in the decades since and you really shouldn't capture to 16 bits any more.
If you record at 16 bits of depth you are pretty much automatically forcing your engineer to choose between quality and range when they are normalizing the recording.
If we want the best quality end product, free from low-res artifacting, we need to preserve an excess of resolution all the way through production until the final export. Exactly how headroom much is enough? Enough that artifacts arising from insufficient resolution are not perceivable in the end product.
Recording close-mic'd drums to analog tape is actually a useful technique when maxing out levels because analog tape saturation can be aesthetically superior to digital peak limiting for shaving drum peaks — analog tape saturates high frequencies first. It wasn't uncommon to either record basic tracks to analog then transfer to Pro Tools, or even to track to Pro Tools then bounce the drums out to analog tape and back.
For the record, there were loudness wars back in the vinyl days, since it was seen as important to have your 45 rpm single "compete" with others in the jukebox. It wasn't something new in the aughts.
> If analog recording captured a much more flexible dynamic range
It doesn't, especially not in comparison to modern digital. Dynamic range is not a strong point of analog because of tape hiss.
The issue with low res digital is that truncation distortion is non-harmonic (not an integer multiple of the input frequency) and so is disproportionately aesthetically damaging even in small quantities — in other words, digital grunge sounds worse than tape hiss.