First of all: You may well be right about the cost!

Of course, to solve the biggest problem on the planet, absolutely massive amounts of resources may be the right size investment.

The way I imagine this to work is that a future MOF material spontaneously accumulates CO₂ molecules from the atmosphere. When it's "full" the CO₂ is extracted (this may be the hard part), and pumped underground (this is mature tech).

If you can go through this cycle without destroying the MOF, it seems pretty sustainable to me.