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They aren’t coming from inside the event horizon, but rather from close to it. Much like the water in your bath tub doesn’t simply flow directly into the drain - but rather swirls around it - matter will tend to do the same with a black hole (or really any object with mass). Consider as well that a black hole that doesn’t spin (a Schwarzschild black hole) probably doesn’t exist. So you add frame-dragging into the mix as well and you have even more reason to pull matter into the plane of spin rather than directly into the black hole.

Now when we talk about Hawking radiation, this is where the quantum world meets the observable universe in a weird way. Those quantum effects (essentially random particle-antiparticle pair creation) happen everywhere, but at the event horizon of the black hole, they can happen in such a way that they become real (rather than virtual particles), sending a particle of matter or antimatter flying off away from the black hole (just outside the event horizon) at close to the speed of light. The larger the black hole, the more surface area there is for the event horizon, which is the only place this should ever happen.

The reason you aren’t getting anything out of the black hole’s event horizon is that inside that, time itself points toward the singularity at the center. So it isn’t a matter of coming up with sufficient power to escape since the future itself - from the perspective of the observer inside the event horizon - is toward the singularity. We can normally distinguish between our three spacial dimensions and a time dimension, but the interior of the black hole is such an extreme environment that all must be considered together. You can no more go from inside the black hole to outside than you can go from April 6th 2021 to April 5th 2021. You’re going toward April 7th 2021 no matter what you do. With sufficient speed, you can slow that journey (from an outside observer’s perspective), but you’ll never reach April 5th. Moving from inside the event horizon to the outside would - by definition - require you to go back in time.