I definitely say go for it! Who cares what unenlightened members of society might think?!
That said, I think it's important to note that a stay-at-home-parent isn't by default also the cook and housecleaner. I have two children, 14 months apart in age. As a SAHM, there was no way for me to stay sane if I was supposed to do it all -- child care (so much more than just making sure they are safe), cooking, cleaning, laundry, meal planning, grocery shopping, bill paying, researching necessary purchases, etc. Maybe the pretend middle class wife of the 1950s was thought to be able to do it all, but parenting is different now. I wasn't about to plop my toddlers in front of a screen so I could vacuum.
Trying to divide the house tasks by who is at home and who is away at work doesn't take into account hours put in. In our case, DH realized early on that it was entirely unfair to expect me to do it all. Indeed, he once said that he doesn't like cleaning toilets, so why should he assume I did -- and he took on cleaning of one of the bathrooms.
Those toddlers are young men headed off to university in another state soon. While the house will certainly be cleaner without them, we still need to take on some of the tasks they've been doing. Since DH is still working for pay, and I'm "retired early", the assumption might again be that the majority of tasks fall on me. I happy to do more, but I probably won't take it all on. No, I don't work outside of the home, but I still put in plenty of hours on other household tasks. I do the laundry (clothes, cleaning towels, shower towels, bedding, throw blankets, dog beds, etc.), plan the meals, do the grocery shopping, cook the meals (and do as many of the dishes as I can while cooking), make the budget and take care of the finances and paperwork, bill paying, etc., keep the household supplies inventories and in stock (medications, toiletries, dog items, cleaners, etc.), I schedule vet appointments and take the dogs, care for the houseplants, tidy and clean the porch and patio, clean our bedroom and bathroom, keep track of extended family birthdays and make sure we have cards and gifts for those and all other holidays that require acknowledgment, clean inside campervan, and many other things. DH does plenty -- I'm not complaining in the slightest. But to think that with our sons leaving that I'll be solely responsible for dog clean up outside, two more bathrooms, vacuuming the house, and few other things is making assumptions about value of the person who does paid work and the the lack of value of the person who does unpaid work.
With two little ones, you probably won't be able to be the sole housecleaner, etc. But you didn't say you're itching to be a housecleaner, you said you want to be a stay at home dad. So do that, and figure out the rest once you see what kind of time you have.
(Also, as someone who has had to learn not to reclean things that aren't to my standards, I will say that's 100% on the other person if they can't accept an honest attempt.)