First off I will apologize for my rant above. Was one of those rare days I got surrounded from all sides
(thank goodness, very rare). I love to teach people this trade, thought it is not for everyone. My hope is to throw out some ideas of what works for me. It's up to you to take it or leave it, agree or disagree, and go on. Mine to do the same with yours as well. So............
Larger parts will generally always get a center drill. Depending on how far out of the chuck they extend determines a lot. Set up rigidity, etc., etc.,...
One reason for 'bumping' just the center in on small diameter parts is at times it will keep the center just far enough out for clearance for the tool. I use a regular live center. Again, this method I use is for short, small diameter parts that just need a bit of support, usually not more than an inch or so out of the chuck. Any more than that you need the full support of the center drilled hole. HTH.