I have an old Albrecht 5/8" drill chuck, needed rebuilding badly when I picked it up. Got that done, there were no real issues with the chuck other than incorrect lubrication, lack of care, and mild abuse. The cheap arbor that was on it was bad, and I bought a genuine Albrecht R8 arbor for it, ~$60 IIRC. It now has .001" runout at the jaws and .002" four inches from the jaws. Great drill chuck, cannot say enough good things about it. Albrecht arbors are the only way to go for a chuck you care about being accurate. Just take a deep breath and go for it! Well, not the only way to go, Jacobs N series ball bearing chucks, made in the USA, were also finely made and accurate.I prefer a separate arbor as well, mostly because they allow for more mounting options. However, Albrecht chucks with integral shanks are said to be more rigid and accurate, with better balance and improved headroom. They are also cheaper than buying a separate chuck and Albrecht arbor.
I think the mount is less important than the quality of the chuck and arbor. When fitted well, an accurate chuck like an Albrecht will be just as accurate as an integral chuck or very nearly so. Of course, there is the human factor - some bozo hitting the poorly installed chuck with a hammer to align it and so on.
I didn't know that, Mike. Thanks, though I will probably never need the warranty...Not to mention that if an Albrecht chuck ever spins on an Albrecht arbor, Albrecht will replace both for free, for life.