During the time I was a tool and diemaker, drilled tens of 1000s of holes and most were drilled in a drill press. The tapped and dowel holes were laid out w/ a square, center punched
and the center punch was picked up w/ a small, flexible drill. The only time a center drill was used was when a vertical mill, lathe or radial drill press were used. The reason a small flexible drill was used to pick up the center punch was that it could be moved until it didn't flex which signaled that the drill and center punch were aligned. This was achieved quickly. The dies we built had build time estimates so the fastest methods were used including the fastest ways to drill the many holes. If the holes had to be accurately located, a jig bore was mainly used or a Bridgeport mill was sometimes used.
Of all the holes I drilled, rarely was a center drill used.....Fred