For the umpteenth time: Black Holes do NOT suck.
No more than the Earth "sucks" a person who jumps off a cliff to the ground.
Secondly, it's "possible" 24th century ships have strong enough and powerful enough gravity generators and structural-integrity-fields to negate blackholes' gravity forces. Not too much of a stretch for a society that had the technology to give Einstein and Netwon the finger and do things like move faster than the speed of light and convert people's mass into energy, transmit it, and then turn it back into matter again.
So, yeah, they just *might* be able to negate the gravity forces and spaghettification effect on black holes.
Why Vulcan wasn't simply moved to the otherside of the hole? First of all, its mass was being used to create the blackhole. Secondly, the blackhole pulled Vulcan in from the inside out. A very different occurance than stepping through one.
Now on a related topic, depending on how you want to look at warp travel it may not be possible for a starship to escape a black hole.
Black Holes have tremendous gravity. So tremendous not even light itself is fast enough to escape it. So once you're "in" a black hole you cannot get out of its influence.
But, you say, starships can move faster than light so they MUST be able toe scape a black hole.
Well... maybe. There's two ways to look at warp travel. One is a more "Newtonian" way of looking at it. That its powerful enough to push a ship faster than light in the physical universe and somehow the length and time effects suggested by Einstein are negated by other systems. If this is the case then, yes, a starship could escape a black hole.
Then there's the concept that warp travel doesn't take place in the "real" universe but in a "sub space" where more feasable speeds translate to FTL speeds in the "real" universe. That's to say that at even Warp 9 the Enterprise really isn't moving at 100s of times the speed of light it's moving at, say, 1/2 the speed of light. But the area of subspace that it is in makes the distance between "point A" and "point B" shorter so that 1/2c translated to a many multiples of C. (Think of moving from the outside of a circle to an inner arc.) We also have to assume that other systems still somehow negate the effects of time at moving even at a fraction of C.
If *this* is the case. Since then a ship cannot escape a black hole because it cannot move faster than light. Although it may be possible the bending of space to get into "subspace" means being able to escape a black hole's influence.