To put it plainly: that's adding another layer on top of the current design to fix an existing flaw.
Right now we have two problems, neigbourhoods suck, and specialists suck. The first problem is being caused by the fact that having more population is worthless, while the second is inherent. By making having a higher population worth it, we fix two problems. But if we simply increase the number of specialist slots with a nude mechanic we've fixed one problem without addressing the second, and to make matters worse, it took an additional layer of complexity.
Now I'm not saying adding that ability to neighbourhoods is a bad idea, in fact I'm fond of it, but the best solution 9/10 is the simplest one.
Yeah, I think that neighbourhoods (and urbanization as a whole) are really one of the biggest lacking features in civ right now. There's not enough value in high pop, and it's compounded right now in that at a certain point, population is simply bad. Like, why would I ever want to grow my city from size 16 to size 17, when I lose an amenity in the city, and all that I get to work is a stupid specialist for like 2 science?
Really, I think what would fix neighbourhoods are multi-fold. They should be districts that you absolutely want to build in every city in the modern eras, so I would probably do the following:
1. Any district next to a neighbourhood has their specialist yields doubled. Thus, you want your neighbourhoods next to every district if possible.
2. Specialists in cities with neighbourhoods should consume less resources (food and amenities).
If you did that, even if that second boost came from the buildings, that would go a long way. So even if you keep the same buildings, make the shopping mall provide, say, 1 amenity per 3 or 4 specialists working in a city, and the food market provide 1 food per specialist, so that both food and amenity for specialists were cut in half. In that way, every city would essentially need to build 2 neighbourhoods to get the full boost there. It would also be a neat balancing mechanism - those mountain campuses give great adjacency yields earlier in the game, but they have less nearby tiles so maybe you can't put a neighbourhood next to them to gain the late game yields.
I mean, maybe even that's not enough. You still get diminishing returns once you run out of districts in a city. But if we make neighbourhoods/urbanization truly change up the late game calculations, that would be a good thing.