I think you are right, we need rockets to get to the Asteroids much faster and efficient..
The way I see it, near earth asteroid mining will lead to a gold rush in the main asteroid belt which means investment in propulsion research. From there they will start casting glances at the Kuiper belt. By the time the Ort cloud becomes a reasonable goal, we’re half way to Alpha C.
Gotta wake people up to the fact that mining and manufacturing in space is the way to go.
If we can get to an asteroid for mining we could also use the asteroid to hop a ride to other parts of the solar system or even beyond and save lots of fuel getting there.
I’ll bet I’m the first person to think of this!! ;)