Maybe, but we would probably have to wait a looong time.
The problem with cellular is tower load. In theory, LTE should be fast enough, and latency is low enough that it can replace landline wired internet. However, carriers tend to overload their towers (a lot), so in the end, in some areas today’s LTE speed feels more like a good 3G speed (and 3G bandwidth is even more oversaturated).
Let’s just say I won’t ditch my fiber home broadband anytime soon.