The experience I have is that drill chuck arbors are soft where the gap between chuck and machine is. This means that over time even the most carefully made arbor may end up causing run-out, Most of the ones that were bent at work where clearly bent as the fitters swung a large radial arm around and thumped the chuck against a bolted down vice, but some had small amounts of bend from general wear and tear. The chuck arbors were regularly removed to be replaced with Morse taper drills.
Since the arbors were effectively a throw away and replace item we just got cheap ones. Drilling with twist drills is not a precision process, If you want accurately sized holes or straight holes other processes such as reaming and boring need to be employed.
Personally I never use a drill chuck in my R8 spindle. I use an R8-ER32 collet chuck, the collets hold the drill much more securely so the drill never spins in it and it is far more rigid than a tapered drill chuck arbor. For smaller drills that the ER32 cannot grip I have an ER11 holder on a Ø16 parallel shank and a Ø16 R8 collet.
Martin C
Martin C