Susskind's book does also mention that the event-horizon shenanigans are due to coordinates and not a physical thing. Certainly I'd trust what he says rather than me, so sorry if I was misleading.

(If anyone has the book, it is chapter 6 section "Interchange of Space and Time Dimensions at the Horizon" and the following section points out the singularity is a time (and you can't escape it (in a Schwartzschild model at least) just like you can't escape time). I'm sorry if my wording is still incorrect.).