I'm not sure of that.
I've created a game with all the services "out" the green influence to check by myself the fact that green influence is only for land value and not the providing of the service.
I also do this map to check some strange behaviour whit education, or the information reported by the info views. The cims appeared to be educated by university first, then elementary school and later by high school.
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I put all the education center at the same time. The colours indicate different ratio of educated people but not in the order "elementary/high school/university".
Also the various number in the windows are not clear for me.
For the university, before this screen but it's practically the same on the screen, i had a high amount of % graduated citiizens by any eligible, and also still 0% High educated.
Perharps the is no bug and don't understand the gameplay mechanic but that appear to be strange for me.
I believe part of the problem is while you have sufficient number of seats in all three school types, you've placed them quite far from the residential zones. I believe, well suspect, that the green lines on the roads indicate the "range" those schools can draw from, and none of them reach your residential neighborhood(s). Simply having sufficient seats isn't necessarily enough, but access is required.
There is still a problem in allocating schools that I've yet to wrap my head around to obtain optimal education throughput. If I have a sizable high density residential zone I needs LOTS of elementary schools to provide sufficient seats and "cover" the area effectively. High schools are a bit easier, but even there, while I know my usage bar is just in the green, I still need more high schools than feels appropriate, which also stresses my school budget. For Universities, in my current city of ~130K, I have three spread around the map with pretty good availability. So I honestly think the limits on student seats in individual elementary and high schools is perhaps too low.
As an aside, I built one residential area with low density housing using a cul de sac model, which looked really pretty all built out, reminding me of subdivisions I've seen in the US. However, because the road lengths with all those curvy cul de sacs, the homes at the periphery could never quite be reached by those green "access" road markers, and the the lots themselves were quite small, so I couldn't really place an elementary school any closer. I guess they're destined to grow up in a beautiful subdivision, but only employable as unskilled industrial laborers when they grow up. Which is too bad, because the development looked really cool.