000646,
look a bit later in siman 37, I think se’if yud, that the shulchan oruch paskens that its a mitzvah for the father not to do so. There is a machlokes between the the bais shmuel and the chelkas mechokek whether the shulchan oruch paskens normally that its assur or if its only a mitzvah not to but not assur, but there is certainly at least a mitzvah not to.
the fact that if someone did so it works and she becomes an eishes ish, and yes that kidushei biah works too to make her an eishes ish – doesn’t mean that its encouraged or that chazal thought it was a good idea. In general the gemara says that nobody should be mekadesh with biah even with an older girl.