You can have the 5-minute walk rule...as long as your child has no particular interest or passion in any outside activity. You can just sign him up for whatever happens to be close. He wants dance? Too bad! Karate's what's close. Gymnastics? You have to be kidding me. Gymnastics is pretty much never within a 5 minute walk of any homes because it require cheap light industrial-type land to have a gymnastics facility. Music lessons? Sorry, you have to go to the terrible guitar teacher because there's no piano teacher near.
And how about adult activities? Marriage? I guess you can marry someone in one of a couple of nearby firms. Forget about compatibility. What matters is the 5-minute walk to work.
Real people with real jobs rarely work in such a close radius from any single place, much less a place where they want to live.
If you have no hobbies except getting drunk, eating out, and maybe seeing a movie or, a very distant possibility, seeing a live show of a very certain type (say, the playhouse where there are also orchestra performances, OR a big live concert venue), you can do that. If your favorite group comes to town and happens to pick another venue, then you'll get an Uber, right? But what if you have an actual interest or hobby that isn't the lowest common denominator. It's a specialized interest for a specialized group. Other than the ease of overeating in many different restaurants and getting drunk in many different bars, the whole POINT of living in or near a city is that you can find many different "clans" for almost any interest. But at most, you'll live within a 5-minute walk of 11,000 people (assuming that the area is the densest in the US in terms of population, which never happens near employment centers, AND you get all green lights) and more realistically within a 5-minute walk of closer to 6,000 people, tops. Do you really think you can find or create a Battle Bot club in a village of 6,000 to 11,000 people? A drone club? A modern board game club? Even a photography club? That population can support some general interest groups (like darts and pool, or poker or mah jong), but it can, at best, scrape together to make one or two special-interest groups, out of luck, chance, or similar socio-economics. Oh, you don't like Magic the Gathering? That's too bad, because you get that and amateur robotics in this near-university neighborhood. Find open night poetry mic night unbearable and have no interest in spiritualist lesbian activism? Sorry, that's the neighborhood you live in, so that's what you get.
And forget actually living like a responsible adult, who carefully makes a weekly shopping list and might choose to visit two or three different grocery stores (one has the best prices, one the freshest produce, and another that weird specialty ingredient). Can't do that with the 5-minute rule. It takes 10,000 people to support a grocery store with the kind of product choices that people want. Even if you're a lousy cook and careless with your money, if you have even one shred of time-management, you shop once a week--and good luck doing that for more than 2 people if you walk or take public transit, because it's not happening. Daily shopping only occurred parallel with daily deliveries and stay-at-home wives, who HAD to stay at home because home maintenance and food preparation took up to 13 hours a day before the 1930s. Cold storage was unreliable, so you had to get fresh food frequently, or you'd get poisoned.
You're living in a delusional world that only is of interest of the TV-bars-and-restaurants singles and (rarely, only if the moon aligns) couples crowd with your 5-minute walk. If you have no real interests, and you do no planning, then living near the only things that give you pleasure (bars, restaurants, and shopping) is of high interest.
What a sad, narrow, pathetic little life.