As we all hopefully learnt from COVID-19, slowing sufficiently is the same as stopping. It’s a numbers game. Slowing transmission below some threshold will eventually mean that there are no new transmissions.
The only reason we haven't eradicated TB is because we've failed massively in getting the vaccine to people in the poorer parts of the world. We could eliminate it just like we did smallpox, the only barrier is actually doing the damn thing. It is made more difficult by the fact that it has a rather long latent infection time, but again, could be solved by vaccinating everyone.