The idea of carbon offsets through payments is that instead of reducing your own greenhouse gas emissions, you pay someone else to reduce theirs instead.
Emission certificates are traded on open markets, where the price is determined by supply and demand. When few people want to buy emission certificates and a lot of other people have cheap ways to reduce their emissions, then those certificates are cheap.
Currently those certificates are cheap, because there are very few industries who are obligated to buy them. In most cases carbon pricing is either voluntary, or on artificially reduced prices.
But if a lot of people would have to buy emission certificates, then that market balance would change. The world industry will run out of cheap ways to reduce carbon emissions. They will have to start tapping into the real expensive methods. Like atmospheric carbon capture or forestration, and the more expensive forms of renewable energy.
That means the price for emission certificates will increase a lot.
So no, global warming is not a problem which can be solved by just moving money around. It has to be solved by making radical changes to how humanity satisfies and/or reduces its still raising energy demand. And those changes will change the lifestyle of the average household much more than the equivalent of $200 per year and person.