I like being a parent much more than being a breadwinner. Working in an office, commuting, sitting in front of a computer, climbing the ladder, meetings, deadlines, office politics, fighting for promotions and raises and bonuses, OKRs and KPIs, insane pivots to chase fads, the constant fear of layoffs hanging over your head... It sucks. The only rewarding part is coming home to my partner and child.
I much prefer cooking, cleaning, and parenting. I would choose being a full-time parent in a heartbeat over my career if I had the option. But due to my particular skills, my earning potential is much higher than my partner's. It wouldn't make much sense for us. So I slog it out so we can afford what we need. She works too, but not full-time.
But so much of what you talk about is foreign to me. My partner and I have no concept of "my own money" vs "my partner's money"; it all goes into a joint account that we both control and we trust each other to spend wisely. And yeah of course we both share the housework and childraising (because that's table stakes for an egalitarian relationship). I don't just come home from work and play video games or something. Seeing my kid grow, play, and copy me is the biggest external validation I could ask for.
If you value your income more than your kids, then you either shouldn't have kids, or you should marry someone who prioritizes domestic work and parenting over their career. But then don't think they're not pulling their weight just because they earn less than you.
That said, I think if the government wants to encourage more babies, it should pay a basic income to stay-at-home parents, something perhaps comparable to the cost of daycare. Then maybe people like you won't consider it unpaid labor anymore and it will become a more respected option.