I agree with Mike, if it is already on the lathe, it's just quicker. Most of the things I drill on the lathe require the hole to be drilled "in line" with the piece, so drilling on the lathe helps with this. Dull drill bits drive me crazy so I've been hand sharpening drill bits and found out it's not as hard as I thought it would be, lots of info on the interweb.
Neal, sometimes I start the hole with the quill and when the hole is about 3/8ths or so deep, unlock the tailstock and push the tailstock toward the headstock to drill the hole. Pulling the tailstock back to clear the swarf. Main point of safety is to always hold onto the Jacobs chuck in case it decides to come out of the quill.
When you had to change out your quill and lead screw, what were the symptoms, and where was the wear?
cc