There are two main kinds of carbon markets: voluntary and mandatory. Mandatory markets exist when a government passes a law that institutes a quota of emissions for covered companies (much like you describe above).

Voluntary markets involve carbon credits being purchased by companies in what amounts to marketing: companies can claim to "carbon-neutral" or more environmentally friendly products and services because they have purchased offsets for the carbon produced by the company. These credits don't involve a quota. Offsets might include reforestation projects or direct air capture of carbon or many other things.

I love the idea of involving micropayments in day to day life, but I think carbon credits might be difficult to apply to individuals. Quotas in general don't work well, imo. And it feels like you'd be trapped in an endless game of whack a mole as people try to game the system.

Also, the freedom-lover in me is screaming that this would be really hard to implement without giving a ton of power to governments -- which I'm not too interested in.