Thermodynamically speaking, the energy in tides does come from Earth's rotation. The moon raises a bulge in Earth's crust and ocean. Earth's rotation carries

Thermodynamically speaking, the energy in tides does come from Earth's rotation. The moon raises a bulge in Earth's crust and ocean. Earth's rotation carries that bulge ahead of the Moon's position. The bulge pulls the Moon forward (raising it to a higher orbit), while the Moon pulls the bulge backward (slowing Earth's rotation.) Once Earth's rotation slows enough, tidal lock is reached. Then the tidal bulge stays in a single place always pointed at the relatively non-moving overhead Moon, and there is no motion to extract energy from.