Why is it not worth it? You're not giving an argument here, just stating an opinion. I don't think every Eurekah is worth it either, I often times don't build two Galleys for example, nor do I build a fort in most of my games, because they have close to zero economic benefit. The housing from a Neighborhood however allows for more pop, meaning more centralized production, which is literally your bottleneck for space victories. I reckon building one aqueduct, one neighborhood and six farms is almost a must in most games, though the Neighborhood is the least valuable of the 3, simply because it comes online so late. I skip it in maybe 1/10 or 2/10 games.
The first question at hand is, is it worth it to build a neighborhood for its own sake? Another way to ask this is - is it worth to put your Production (and a presumably high-Appeal tile) into producing additional Citizens? That's really what you are doing when you build Housing. The answer is not really, because after 10 pop, it is better to put your production into something else - e.g. military or Builders. That's something objectively provable with math. That includes centralized production. You see that Royal Society and that clump of Woods tiles? That's my centralized production.
Now, granted, I could be wrong. You'll just have to back up your argument with math to prove it. Check the bottom of the post, I'm working on the math myself - again, could be wrong. But it is math, not opinion.
That's not what we are arguing about. I never invest more than necessary for Eurekahs/Inspos into housing/food, as I've stated three times now, so bringing up this argument is just futile and unnecessary. Please try arguing in good faith. I probably play one of the most violent/expansionist playstyles on this entire forum, you're barking up entirely the wrong tree. In fact, you're not even in the correct dog park.
I'm totally arguing in good faith. You're arguing that it is worthwhile to invest into housing and food for Eurekas and Inspirations, I am arguing that it is not worthwhile. By all means, change my mind! You'll just need to do the math.
The only thing you have established as a "cost" for growing past 10 is less amenities, which I have agreed is one negative factor. There is not a single other "cost" out there and you know it. There is literally no downside to growing your cities past 10 pop if you are doing well on amenities. And if you straw man "growing past 10" into "investing in housing/food" one more time you'll step onto a Lego piece and hurt your foot.
I'm trying to keep this as calm as possible. I'm not trying to start anything, honest. You are missing one big cost, however -
opportunity cost. The question isn't whether more population is good or bad - it is whether that production is better spent on something else. Is it better for me to spend that Production on Housing, or on military? Or another Settler? Or a Builder?
I popped up a random old save - Turn 182, Hungary, Diplomacy Victory game. All the cities above size 10 have Housing improvements - Aqueduct/Dam/Farm. There's 4 of them (out of 17). They're all foreign cities I captured, either city-states or Spanish cities. 1 of them is mine (Gyor) - it is size 10, has 0 housing Districts (it does have a Granary), and will grow in 330+ turns...that looks perfect in my book.
You're wrong on every level and your smugness is not just unjustified, but kind of embarrassing. You've not only not provided a single succinct argument besides amenities as to why growing past 10 is bad (which was your initial claim, after all), you've strawmanned yourself into a corner and are holding up the flag of "optimal play", and of "objectively better", "spreading misinformation to newer players" when you're simply wrong.
You literally say "you're missing the point" twice while completely missing the point yourself and arguing against a windmill. I don't know what it is you're trying to accomplish, but it's not working.
Growing past 10 population, for all things considered, is in almost every scenario beneficial. End of discussion.
Investing in food and housing is, in almost every scenario, and aside from Eurekahs/Inspos, not optimal play. I'd be the first person to tell you that. But that is completely irrespective of our discussion. These statements are not mutually exclusive in any way, shape, or form.
I'm not arguing that population is bad. I'm arguing its not worth investing in past size 10, even for Eurekas and Inspirations. That's it. I mean, our arguments aren't that different, it really just boils down to whether the Eureka for Conservation is worth getting or not.
I'm looking at Conservation in game, says 1540 Culture. Half of that is 770 Culture. District Production cost is....complicated, but I popped up that Hungary game again (turns out I was 9 turns away from researching Urbanization, perfect!) The cost was 365 Production for a Neighborhood the moment I finished Urbanization. So is 770 Culture worth 365 Production into something otherwise we agree is not worth building? Of course, that's only half the answer - the other half is opportunity cost. What could I be building
instead of a Neighborhood, and will that other thing help me win faster than the Neighborhood? Gyor has its 10-pop District slot open, and has no Trade Route building. It is also finishing a Dam to boost the adjacency of a nearby Industrial Zone. The question is not just whether Gyor should invest 365 Production into a Neighborhood. It is also
should Gyor build something else first? In game, I probably wouldn't think about this so directly. I'd probably look at my choices and go "Ahh! I can get another Trade Route after I finish this Dam!" lock in the cost for a Harbor, and move on.
Like I said, I could be wrong. 770 Culture is a lot of Culture. But just remember the opportunity cost.