Yes, but then you also need to stabilize the antenna platform, either physically, or electronically or both. All that increases the cost vs a terrestrial tower where the stabilization requirements will be lower.

Not saying it would be impossible, it would be a fun and interesting problem to work on, but it would be interesting because it seems like there's a nice solution in there at the intersection of all those problems...

But lte's base stations has actually very limited capacity, thats why in cities there are a lot of micro cells for capacity and much less 'full range' cells for coverage.