All infantry should be able to catch all archers, imagine situation where you have only heavy infantry left against a few light archers, if they wouldn't be able to catch them, that would be an auto win for these archs. Heavy archers are already slow enough, the problem is that infantry is too slow to catch them fast enough to not die from a crossfire.
Maybe throwables should slow down enemies a bit for a couple secs on hit and maybe they should even rear cav on a clean headshot throw to the high speed horse.