Couldn't you bury the plants, the same as trees, sequestering the carbon underground?

You could do that. It is how most fossil fuels got underground in the first place. OTOH if you have the ability and available energy to bury all of that plant matter, maybe you could instead just convert the CO2 directly to carbonate and skip the part with the plants.

If you have the energy to distill a large proportion of the earth's atmosphere you have enough to crack the O2 from the C and not mess with plants etc.

True, and I had not considered that. I like the idea of growing more trees though.

Trees = good, I'm with you.