Development costs are far from their lowest at end-of-cycle.
That's exactly when the prototype development kits come out of small scale testing (maybe tens of units, all incredibly expensive bespoke units, probably hand soldered and assembled), production ramped up a little and the evaluation kits are produced and distributed to first party studios and large third party studios, with thousands of consoles produced with the expectation that their lifespan is likely only going to be 3-6 months. These are then extensively tested by developers, both to see what needs to be done to get their launch titles actually working on the machine, but often very serious hardware bugs are found in this period that may require fixes to the chips themselves or software workarounds that affect performance. For some of the recent console launches there have been 2 or 3 rounds of evaluation kits in a year, and the previous evaluation kits are effectively bricked.
After the evaluation kits seem to have converged on a final product, the development kits are produced to ideally match the final version of the evaluation kits, but again these are tested before production is ramped up because some things do change (most trivially the case, even if the board is fine). At this point tens of thousands of dev kits are produced, each different enough to retail kits (more memory, maybe extra ports, etc), usually at least 6 months to a year before console launch so studios can make a final push on the launch day or first quarter titles, and in the background the same evaluation process for retail kits (usually just stripped down from the development kits, but usually different cases etc) starts, and eventually a final design for the retail product is produced that's good enough for manufacture.
This time is definitely not just when the console manufacturers kick back and rake in their profits, this is when they're already spending big on the final push to get to the point where they even have a new console to start a new cycle with.
Separate to the console manufacturing side, the years before release are when big money is spent getting studios on board to produce launch titles, because without those, the console will be dead on arrival.
TLDR: revenues at the end of the console cycle aren't funding the next generation, because it's probably already been in development since the launch of the current console, rather those end-of-cycle revenues are hopefully paying off the gamble they took funding development for the current generation.