I've had game/leghorn cross birds. They did well. Laid in season, some went broody with age, some didn't. Lots of instinct. I'm going to have more soon. have some wyandotte game crosses now. Too broody, not that great at brooding, not much instinct. Pretty though.
They are all born with roughly the same amount of eggs in their ovaries. They all lay the same amount over their lifetime. Birds that lay 3 clutches of 12 each year will live a lot longer than birds that lay 360 a year.