fessick

Yep. Along similar lines of thought, there's the issue that the equations and laws governing classical mechanics fall apart in such settings.

Even so, assuming that we can apply classical thought to the problem: the simplest roadblock to rockets escaping from a black hole is that their change in mass per time unit multiplied by their velocity must at least partially exceed the gravitational pull.

Either you utilize ungodly amounts of fuel per second or you already have a crazy-high velocity or some combination of both. The math just makes it infeasible. There's limits on mass you can have and eject, and limits on attainable speed.

"a rocket takes off. let's say it's going upwards at 1 m/s at some short time after takeoff. why can't it then reduce (not to zero) acceleration such that it stays going upwards at 1 m/s all the way out of the gravity well? don't aim for escape velocity, keep the velocity at exactly 1 m/s until you're out." <-- that will totally work, but isn't escape velocity.

Escape velocity is essentially the velocity an object must start out with to move towards an asymptotically infinite distance from the gravity well without additional thrust. That last bit is what makes it escape velocity. The gravity well will slow the object to near zero velocity but the object's distance will eventually overcome the gravity before it reaches zero or negative velocity.

Your example of moving at a constant speed of 1 m/s is only achievable with constant thrust to cancel gravity, thereby stopping the object from slowing during its ascent. If the object has achieved its escape velocity, no additional thrust is needed. One is not better than the other, it's just a matter of what is more practical in terms of fuel or travel time.