I had the same problem with a 12" bench Delta drill press, and a friend
suffers with two Crapsman drill presses. The problem is that good
chucks are expensive, and would represent a large fraction of the cost
of the whole drill press. So, the manufacturer cuts corners.

I solved the problem with my Delta DP350 by replacing the original chuck
with a Jacobs JT33 heavy-duty keyed 1/2-inch chuck (MSC #08590093, $84).

All good stuff and I just saved your entire reply in my notes.

Just so I know, if I do have to replace the chuck, why would a more
expensive one make a difference with slipping bits? By that I mean what is
different mechanically about a premium one ? Do they have ridges that grip
the bits or something ?

Thanks !
JCD