I've done some further googling and found some studies on the topic, though on-land: https://cbmjournal.biomedcentral.com/articles/10.1186/1750-0... and some more from a presentation https://www.feem.it/m/events_pages/20167111127315Zeng_presen...
Though the question still remains how securely the CO2 would be stored under the ocean. Maybe with a large enough layer of rock on top it would suffice.. I suppose it's high time we started field trials on all these approaches.
My own back-of-napkin calc says that we'd need to cut about .1 to .2 % of tropical rainforests per year and remove them from the carbon cycle, not sure if that's right.
It would be as if someone started doing research on vacuum tube transistor technology today if we were having a global compute crisis and we also had limited amount of sand with which to make glass and sand was an essential resource in all sorts of other things like the food supply chain.
What impact on cities? Cities take up almost no space and are irrelevant when talking about planting forests and then sinking them in the ocean. At worst there will be more freight train noise.
Someone who threw a ton of venture cash at "Air Freight Ltd." in 1913 or whatever would have lost their shirt.
Back to the point: I'm not saying this won't work. I'm saying that there are firm limits to how well it MUST work just to be better than technology that was proven out five millenia ago. That's a really high bar, and it needs numbers and not press hits.