You already can, plant trees or other plants or use algae farms etc. Then sequester the carbon into something that will not decay quickly and release it back.

You already can, plant trees or other plants or use algae farms etc. Then sequester the carbon into something that will not decay quickly and release it back. The problem is always scale, so any artificial mechanism that would mimic this would have to many orders of magnitude more efficient than using existing biological solutions to be viable as biological solutions are simpler and cheaper to do at any scale.