In regular Factorio, the challenge of pre-Aquilo biter eggs is that you need to capture a spawner somewhere inconvenient. Either you've dealt with the pain of keeping a spawner alive near you all game until you get to that point, or you're going far away to capture one. Since that kind of challenge doesn't exist in seablock, egg mutation is intentionally a bit of a pain to get you the handful of eggs you'll want for things like prod 3s and biolabs before Aquilo, and then to give you the eggs you need to to eventually start a captive spawner once you have the tech. Personally I got my labs all upgraded to biolabs pre-Aquilo by, as you said, somewhat "babysitting" the process. And if you really don't like the idea of shipping live pentapod eggs, you can always accept the (significant) efficiency loss by shipping biolabs then recycling them when you need the eggs.
With that said, I personally don't really bother much with productivity 3s until post-Aquilo, so I appreciate the feedback that if you are someone who makes them in large numbers at that point in the game, egg mutation probably feels a little too painful. The idea is, as you correctly deduced, primarily to give you a challenge to bootstrap your eggs on Nauvis.
I don't really like the idea of moving captive spawners earlier in the tree, but I can get behind the idea of some kind of recipe where you can turn biter eggs into more biter eggs at the Argicultural science level. I just think it would be important for such a recipe to be "bad" enough that you'd never seriously consider it once you get captive spawners, as that's supposed to be the real way of doing it. Generally the "bootstrap" recipes in the mod are all intentionally very bad so that they'd never be realistic to use long-term (personally, in my first Space Age playthrough I kept using Simple Coal Liquefaction on Vulcanus long after unlocking the better one because it was doing well enough and not worth the effort to change my setup). The main difference here is you get the bootstrap recipe long before the real one.
Maybe something like 10 Biter Eggs + 2 U235 + 10 Bioflux = 11 Biter Eggs, in a Biochamber, with a 60s crafting time (really 30s because crafting speed of 2). Maybe the biter eggs are also 50% spoiled (regardless of input), so much like pentapod eggs you can keep your eggs fresh as long as you keep cycling the recipe, but the output is automatically less valuable than a captive spawner?