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There already are restrictions about how low and where you can fly a 'real' airplane. There is even a regulation that would keep an airplane from flying over your house at 500 ft. under most circumstances. The reality is that most pilots don't want to be 500ft above terrain unless they are VERY close to the runway

There are also plenty of good reasons to be under 2,000 ft. The most general is that all training and approach for VFR ops at airports is done at 1,000 ft. by default.

Airspace and altitudes are pretty complex, for a more involved example: A VFR flight departing North from Boeing field in Seattle HAS to stay below 1800 ft but above the highest parts of the city at ~750 ft. Because the air-space above 1800 belongs to jets on instrument approach to Sea-tac. In other words, to get out of that airfield you have to fly underneath the 747s. Seattle is just one example, there's weird airspace like this that balances the needs of different users just about everywhere.