The trouble with vaccinating people most likely to spread it, at least as I've seen it explained, is that you have to vaccinate a lot of people in order to have

The trouble with vaccinating people most likely to spread it, at least as I've seen it explained, is that you have to vaccinate a lot of people in order to have an impact compared to vaccinating the most at risk groups and there's only a limited supply of vaccine and limited capacity to administer it right now. (Also, technically there's probably more evidence of it working to protect at-risk people from severe disease and death than for it stopping anyone spreading it, but that's mostly just an artifact of what's been tested so far.)