You don't need a very high-powered radio if a) you have plenty of time to transmit the data back and b) you can afford to build large receiving telescopes back

You don't need a very high-powered radio if a) you have plenty of time to transmit the data back and b) you can afford to build large receiving telescopes back on Earth. The latter we already do have, although bigger the better, and the former is just a case of patience. Galileo, famously, was unable to fully unfold its high-gain antenna and had to transmit everything via the much lower-bandwidth low-gain antenna. The ability to batch the probe software to use higher-efficiency data encoding and modulation meant this was not as disastrous as it could have been. This failure mode was also likely the reason that both Cassini and New Horizons opted for a more traditional rigid dish antenna.