Yes, You can do it. But in Aereo's case you didn't, they did. They set up a small forest of individual antennas in a central location, then invited members of the public to lease them. It's top down, whereas what you are describing is bottom up.
If you had negotiated the right to hang a dime-size antenna of the Empire State building, with a home-brewed DVR accessible over the net, and then your friends and acquaintances had done the same thing, and eventually you had clubbed together and hired a janitor to keep an eye on the whole thing, so to speak, then it would have been a community thing that aggregated around a single point (a tall building where I imagine TV reception is good). Aereo is more of an astroturfing operation. It differs from your scenario in the same way that a housing subdivision built out by a developer differs from a village.