I'm not seeing how that plays out. Synth pops cost a small amount of alloys to assemble. When pop growth slows to a crawl in late game, you're going to have a huge mallus to bio pop growth from available jobs, which does not affect manufactured pops. Even if it takes 500 points to manufacture a pop, you're still going to there faster with ~8 or ~10 growth per month instead of bio-pop growth of 0.5. The small number of alloys from your monthly budget shouldn't be much of a problem by that point.
Early in the game, robots are still great, because more bodies means more resources. The main issue is that they game now requires a kind of hybrid tall/wide strategy that demands a few core planets and a large amount of unsettled space for automated resource gathering. You just have to be much more careful about what planets you colonize and refrain from colonizing everything you can like you normally would, and/or be willing to convert resource worlds to foundries and factories once you get a Dyson Sphere and Matter Decompressor up and running.