Is there such a thing as a high-quality adjustable wrench? One with high
enough quality that you could use it in place of a lot of ordinary
wrenches, and not have it round/damage the heads of the nuts?

In particular, it should reliably hold its exact adjustment, and should be
exactly adjustable to the nut it's applied to.

Even a Craftsman 2-piece set for $29.99 has a bad review for rounding the
nuts. What brand is better?