An advantage of having a separate drill press is if you have a job set up in your mill (some jobs can be set up for a few days in mine), you need to drill some quick holes that take more accuracy than a hand drill in another job.
A drill press good enough for cheesy work ,neither clean nor accurate,One thing I haven't seen anyone mention, is that a drill presses has a much larger spindle to table distance. A BP size machine maxes out at 18". My 17" floor model jet DP goes up to 29-1/8" , and its over 36" if I swing the table out of the way and set the work on the base. All that extra capacity lets you do stuff like Keith Fenner is doing at the beginning of this video.
https://www.youtube.com/watch?v=UObRO4eQJZo
if you are using a BP style machine you have to start doing stuff like clamping to the table edge, and then rotating the turret & extending the ram.
Another thing to consider is what you are drilling. I do a lot of woodworking, and I don't want sawdust anywhere close to oiled machine ways.
The other main benefit of a drill press, is that the bearings are cheap, and easy to replace, so if you abuse them it's not as big of a worry.
A good drill press is good to have you have a # 2A friend who is a machinist insisted that I buy a floor standing model drill press for my garage shop. I have a Bridgeport, what is the compelling reason why I need to buy a drill press?
Thank you.