Firstly I don't know what you mean by the Friis equation "assumes an isotropic antenna". It explicitly accounts for the gain of each antenna, in the direction of the link, relative to an isotropic radiator. The fact that it's relative to an isotropic radiator is just how all gains are measured. In fact, the antenna pattern doesn't matter at all to the link, only the gain in the direction of the link (Friis assumes no multipath). Whether the receive and transmit antenna are "the same" or "different" really doesn't make a difference.
This is the distinction I think you're trying to make, and which I agree with:
If gain is held constant, link margin improves as frequency decreases because of reduced path loss at lower frequencies. If instead antenna aperture is held constant as frequency is lowered, antenna gain will decrease at the same rate as path loss improves and there is no net effect to the link.
Both answers are technically correct, in a fixed gain scenario where your antenna can grow as large as necessary to hold gain constant, (or the scenario doesn't allow for high gain, narrow beamwidth antennas) lower frequencies will make longer links. In systems where aperture is constant (which is the case for many practical systems) antenna gain will improve as quickly as path loss degrades when you go to higher frequencies, and there is no net advantage at any frequency.