But the naive interpretation of this leads to a singularity, and the fact it leads to a singularity shows that that interpretation is wrong and that there should be a limiting factor somewhere, the article suggests some of them.
As for the black hole, it is hard to argue using that analogy since you don't want to get close to a black hole for very well known reasons unrelated to the singularity, but let's get into sci-fi mode and say you could, it may be risky but it may also be worth it. The thing is: from the point of view of the travailler, you never cross the event horizon, and you get to know what's inside the black hole as the event horizon recedes from you, maybe you will never get back, but maybe there are greater things in there. And we are already trapped anyways as we are going one way through time, just as in black holes, things go one way through space, so maybe it is a risk worth taking.