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I was using my drill press for side milling, and the bearings got wore out. Now when I run my drill press at high speed it runs real loud and I have a lot of side to side play. All of my pieces have to be centerpunched or the bit will wander pretty bad.
But, like others have said they have had no problems with this. Anyhow you said you are making flat bottomed holes so side pressure is a non issue for you.