Yes wax has its downsides, too. You have to constantly reapply it because it will just wear off. Leather boots won't soak up the wax, it is just on the surface and the more you go and use it, the more you have to reapply it.
This is why I prefer leather grease for shoes. It will keep the leather smooth and water repellant, and this will be as good as Goretex. The only downside: When they are wet, they will stay wet for days. Goretex shoes dry within a night. So if I would hike for days and I expect constant rain or muddy terrain I would prefer membrane shoes, too.