I loved having a pool as a kid, tons and tons of fun in the pool with friends and random neighborhood kids.
I found out a decade or two later my dad DESPISED the pool, but not for the money / cleaning / electricity / space reasons - because of the other kids. He felt he needed to be the lifeguard, ALL the time. A lot of parents are pretty selfish / crappy, and their kids would come over all the time to play in the pool, so then he needed to spend all that time watching them, telling them not to run, etc, etc, etc. The worst was it was actually really common to have kids come over uninvited and he'd allow it because he wanted to be nice (or he'd tell them to go home and then spend the rest of the day feeling bad), or even worse we'd come home from being out and there would be kids in our pool (and yes, we had a fence with a locked gate, though its not like it was 15' tall with barbed wire at the top - kids can climb a fence without even trying). So when we moved houses I wanted a pool again, and he shut that down so firmly that it wasn't even a conversation / debate / begging.
The big difference for you though is I grew up in Minnesota, so we were the only pool in the neighborhood, I'm sure it's a different dynamic when half the houses on the block have a pool.
I will agree with you on one thing though, having a pool in your backyard is a totally different experience than going to a public pool. If you want to take a quick dip in the afternoon, you can be in the pool within minutes and zero stress if you have it in your backyard - if you are packing up 3 kids into the car it is likely 30 minutes of wrangling and chaos, not much of a stress reliever. But on the downside, part of the fun of the pool for kids is having a dozen other people in it, so massive upside to the public pool there (and you don't need to play lifeguard...).
The simple reality is part of the beauty of MMM is knowing the math. What is your retirement date on today's trajectory? If you add the capital AND the ongoing expenses to your budget how far back does that push your retirement date? Are you willing to work those extra years of life in order to provide a pool for the kids?
Side note, I think someone said this already, but I'll agree - pools don't make houses more expensive, if you want one buy a house that already has a pool, you seem to be familiar with renting so just buy a new house that already has a pool and add your current house to your rental portfolio. If all goes well its very possible you could end up having the house with a pool you want AND you'd have more cash flow than you have today and an EARLIER retirement date.