I’m sure there are posters here who can address this much more knowledgeably than I, but I’d venture two observations. The first is that the sun’s gravity differential between Earth and the nearby planets isn’t really all that great, and this is reflected in the fact that the orbital speed differentials aren’t all that great. For instance, the Earth’s mean orbital speed is 29.78 km/s, while that of Mars is 24.08 km/s. Farther out in the asteroid belt, Ceres has a mean orbital speed of about 17.9 km/s.
So getting over to Mars or the asteroid belt is, relatively speaking, not all that demanding compared to getting to the sun, and conversely, so is getting back.
The other point is that some of the proposals I’ve seen involve capturing an entire asteroid rich in some desirable metal(s) and basically “towing” it into earth orbit. While this would involve a lot of energy it’s not in the same ballpark as sending something into the sun, and the economy of scale is probably far more efficient than many back-and-forth missions.