Having a lathe one can easily turn their own collet holder with it having a sizable through-hole. and a line-up mark to the same chuck jaw and on the line. This will run much truer than any catalog holder...and it can be tickled at a future time when the non-independent cuck gets a little more off.
Agree if your non-independent chuck runs close enough then a catalog collet holder is OK.
The best collets run .0002, and with them, .0005 to .001 can be a hassle because of other issues.
Making your own or a catalog version, having an Adjust True might be the answer if needing tenths.
When I made the backing plate adapter for my Hardinge I made it with a Set/Adjust-Tru feature. Even if I never end up needing to use it: better to have it and not need it than the opposite.