Front center and chainstay length set your fore-aft weight distribution. If the proportions are right, you get better handling and possibly stability.

Head tube angle affects the tendency of the fork to flop (called flop), and combined with fork offset and wheel diameter determines trail, which is really important in designing how your frame will steer.

FC and CS have something to do with fit, and head angle less so. But, a more laid-back head tube can result in longer FC, so it's not like there's no connection to fit.