I think you're overestimating the complexity of all this. I pay most things via a 2% cash back card. Just the monthly statement to manage, no need for multiple cards, and no keeping track.
I get $500/year back on health insurance premiums alone from that, let alone all the other spending. Everything except my mortgage can be run through it.
Perhaps it's easy enough in America. Where I am, there are multiple rewards programs separate from credit cards. Some shops have their own special card, and some are part of a bigger scheme with a common card. It's all a mess. I hadn't thought of using it to pay for big things like a house or health insurance!
There are certain credit cards with higher rewards at certain companies - if you buy a lot at Amazon, for example, it makes sense to get their 5% cash back card. Target has one as well.
I get $500/year back on health insurance premiums alone from that, let alone all the other spending. Everything except my mortgage can be run through it.