In fact if I understand correctly this is the mechanism for a runaway greenhouse, that is, something like what happened to venus. Warmer temps allow for more water vapor in the atmosphere, due to it being such a good greenhouse gas, temps then build out of control as more and more water is vaporized.
https://en.wikipedia.org/wiki/Greenhouse_gas#Role_of_water_v...
The atmosphere is currently ~422 ppm of CO2, and an average of ~5,000 ppm of H2O, with humid tropical areas having up to ~50,000 ppm of H2O.
Water vapour makes up ~half of the greenhouse effect. It's not a 'good' greenhouse gas, it's just that there's a lot of it in the parts of the world that get a lot of sun - the tropics.
There is also huge amount of natural CO2, single vulcano eruption... It is about reducing green house gas emissions generated by humans. And there are many artificial lakes, fields and forests that generate huge footprint on water vapour..
More seriously though, as the effects of climate change intensify, I think it’s all but inevitable we’ll have to seriously look at manipulating whatever environmental factors we can in order to counteract the worst of them. Maybe we can’t do much about the sea level rise, but maybe it would be possible to moderate storm and drought/flooding intensities. As you pointed out, water vapor levels may be one of the easier things we could manipulate, as least on a local or regional scale.
There's also no meaningful amount of water that can be sequestered, given there's about 10^18 tonnes of it in the world's oceans.