1. People who watched how chaotic it was to get a vaccine at first, and tuned out. They might not know how easy it is to get one now in most of the US, so some campaigning might be able to reach them.
2. People who want to "wait and see", who have concerns that there are longer term effects from the vaccines and want to wait to see if it's fine for other people they know. This might not necessarily just be people who are paranoid. Lots of folks with conditions that suppress their immune system are leery of the vaccine too, seeing how it's laid out some people with no immune system issues for days.
3. People who believe a wild conspiracy theory about getting microchipped, 5g, plannedemics, etc.
A lottery might get some of group #1 to check back in, but so would just better engagement. How much door to door canvassing would $5 million get?
It will have the exact opposite effect on groups 2 and 3, making them even more paranoid. If this is so great and doesn't have real drawbacks, why offer millions of dollars to get it?