Why should they have let him go?
Didn't he break the law? It was more serious that allowing that guy to continue selling loose cigarettes.
It is pretty clear that Finicum wanted exactly what he got. He was interviewed at the site and he said he was not leaving without as fight. So it is likely he would have provoked one elsewhere, and in a place where he was more likely to kill someone. He came to become a martyr, and that is what he did, though I doubt that he will become a very effective symbol for what is an unsympathetic movement.
The main idea of this movement is that ranchers, most of whom are Mormons, using federal lands at low rates should be simply granted the ability to use the land for free and without restrictions. But Oregon, Utah and Nevada do not own these lands, and it would be an added burden to he states to police them. Endangered species would become extinct, the lands would be overgrazed and rendered useless for generations, all for the profits of a very few people whose use of these lands do not benefit anyone but themselves.
It would not have made any real difference to me, to tell the truth. I am simply explaining how the FBI considered their options. I am pretty sure that seizing and holding federal buildings in remote locations would have become a major strategy for this nutball movement.