Maybe this is a stupid question, but isn't the necessary tech "planting trees"?
So, yes, it’s an option. But it’s a slow option we’d need to start implementing immediately if we wanted it bear fruit.
(We produce enough CO2 that it takes 40 billion hardwood trees growing for 40 years to sequester as much CO2 as we make in a year. We’d have to plant a lot of trees, and then not touch them for years, to affect the course of things)
Hence why you need to cut them down and bury.
And, BTW, trees don't stop growing. They keep adding mass in their trunks. Literally the first google hit for "do trees stop growing": https://earthsky.org/earth/what-makes-a-tree-stop-growing
Edit: guess what? They even grow faster as they get older! https://www.npr.org/2014/01/16/262479807/old-trees-grow-fast...
Anyway, the land we have is limited. You literally can't cover the planet in one big forest to capture the gigatons of carbon we have released. You have to do active forest management and store the carbon somewhere stable, for example as biochar.
It's also a while out. We have bigger issues today than "who's gonna suck back out some CO2 once we cut emissions sufficiently". We'll get to that in due time.
For what it's worth, if you have unavoidable emissions today that you want to compensate, and want to also fund the people working on CO2 capturing technology, see https://climeworks.shop for a pay-what-you-want option. I don't really believe in planting trees (which is way cheaper per ton of CO2 it claims to absolve you of), and these machines apparently emit "only" 10kg for every 100kg of CO2 captured (90% effective sounds reasonable), and it's accounted for who claimed which share of the machine's captured volume so it sounds directly effective to me. It's just that the scale is peanuts and will remain so until public bodies and companies start to run out of emission reduction options and decide to use it - but at that point we better have this tech geared up.