Currently nothing is done to incentivize people to stay Covid free.... just the fear ... but even that is not enough
Actually since the vast majority of people in the world is covid free, the opposite makes more sense: some sort of punishment for the ones getting sick.
Of course, such thing cannot be implemented.
Also going by your idea, people should be periodically tested in order to incentivize them and here's a big problem: if they would have funds to properly test everybody periodically, no other move would be necessary, since normally most people don't want to get sick.
PS. There was an idea on the news that US may incentivize people to get the vaccine. That's doable and in line with your proposal too.
Obviously not ALL people would qualify for this, because a $300 per month reward would not incentivize rich people to do it, but the majority of people are poor and they would desperately adhere to the rules, if they would get an extra $300 on their monthly social grants for instance. (The $300 is just an example.... I do not know what different governments pay in grants for the unemployed .... but it helps to explain this)
The US gave "boosters" to almost everyone and those people did not have to "give" anything to receive it.... why not give that with specific requirements like this.
As I said before... we do not live in a perfect world.... but we can look for solutions to deal with this pandemic.. right.