The singularity seems to be a consequence of the existence of a black hole, not a development. By the time the hole is formed, the singularity should be in place from the point of view of any "observer" concerned.

Since the singularity is inside the event horizon, meaning that from our point of view nothing inside happens in finite time because nothing reaches it in finite time,  and the relationship between space and time inside the event horizon is altogether different, or would if we could see the place anyway, therefore, yes, I suppose you could say  the event horizon does make this problem go away! :-)

Cheers,

Jon