Very true. Keep in mind, though, higher power is more expensive.

They've said in the past (I'm failing to find the reference right now) that they chose Arecibo because of the high-gain of the antenna. I believe that the amplifiers that they're actually using above the dish are somewhere around 700 Watts.

Antennas with large effective apertures (of which Arecibo's is the largest) are considered high gain antennas, which have small angular beam widths. Friis' Transmission Equation shows that you could use low-power transmitters, but still maintain high boresight with a sufficiently large antenna surface. :)