On the cheaper table top or bench drill presses, if the spindle runs out a lot, knock the chuck off and clean everything really well. lap the check to the tapered end of the shaft for as good a fit as possible and so it seats square. Take the chuck apart and clean and oil it with a decent machine oil. I think you will find that everything works better. Not perfect but better. All this Chinese stuff has to survive being on a ship at sea for a long time, so they use stickier, more crude types of lubricants and such as antirust agents, like the old stuff they used to paint on machines that had to be cleaned off before use, cosmoline?? ( Spell check doesn't know how to spell it correctly either!! ))
Type at you later,
Dan McEntee