Ashtagon, composite bows are indeed stronger and easier to carry around because of their smaller size. But nothing prevents you from using a 190lb longbow just like a couple of the Mary Rose ones.
You'll have to face bone deformation though, just like some skeletons that were dug up.
Its size may increase and thus the strength needed to pull it. In a world with strongarm bracers and gauntlets of ogre strength, this isn't a problem.