Nobody's pursuing such initiatives. Doing so would be even more expensive than net zero emissions policies.
We definitely need to start pursuing it, at least researching it. We'll never solve the climate change problem with emissions reduction alone, recapture and sequestration will be essential.
There are some strategies which are pretty cheap, such as planting forests. But the numbers don't add up on that; we'll need more. I think carbon recapture systems may pair fairly naturally with renewable energy generation, though. Renewable variability means that in many cases it makes sense to overprovision. For example, in order to get sufficient power generation from a solar plant on cloudy days, you may install 2X-3X as many panels as you'd need for a sunny day... but that means that on sunny days you have lots of excess production that might be hard to use (I experience that with my rooftop solar; last month I generated just over 1 MWh that I couldn't use and the grid wouldn't pay me for). Using that excess to power carbon recapture would be a good idea.
For that to work, though, we need to arrange some financial reason for people to build and operate carbon recapture systems. That's a big missing piece which only government can solve. The obvious solution (to the entire climate change problem, actually!) is refundable carbon taxes plus carbon tariffs.