I agree that NC is odd (even to me) in the way some things are done, although from what I'm gathering many southern states are done this way vs most of the rest of the country. From what I remember, Ohio is done more how you are thinking. (I grew up in Ohio). Actually the town I picked to live in in the Charlotte area has, from my understanding, the best school system in that area and one of the best in the state. Even though I don't have kids that was important to me more for resale value of the home. The only thing Mecklanberg county has done with taxes to help with the public transportation system is that added a temporary small amount to the county's sales tax to help in getting the money to build the first light rail line. If remember right that tax was for maybe 3 years and not renewable. I do remember that it passed. They have not asked for a sales tax increase to help build the 2nd line that I am aware of. Actually found some of the road stuff due to the stimilus package and NC getting some of the money for a couple of specific projects. There were some major issues because Raleigh was not going to send it where it was supposed to go, they were going to use it for who knows what and the federal govt had to step in and by pass Raleigh and send the money to the locales where that money was supposed to go for specific projects. One of which is in Huntersville (just outside of Charlotte). They had put together a request for some of the money to redo a really bad intersection. It was approved as one of the projects to get the money and Raleigh didn't want to send it to them. They did get it and from what I read a few days ago that project is now just about finished and the intersection looks like it should now work much better. There were a couple other projects in Charlotte that the fed govt had to make sure they got the money instead of Raleigh sending it to other areas. Actually I think one of those projects that the fed govt had to make sure got it's money is actually the 2nd line of the light rail that looks like it's close to getting started with construction. One thing that I know property taxes are used for is parks and recreation areas. Over the past 10 years, Mooresville (where I lived) has upgraded and added new parks, including a skate board park, which looks really cool. When we moved one thing the town was seriously looking at for their next major project was adding bike lanes or paths to certain roads. They were supposed to be doing a feasibility study on it.
Just out of curiosity I found a property tax calculator and put in what my home is worth and checked different areas of NC (which are pretty similar for the most part, where I used to live is less than anywhere else and those are all virtually the same). I think used it for several areas of Ohio with the same price. The city my parents live in is less (it's also one of the most depressed areas in the state, think not recovered after the steel mills shut down) and every other city I put into it came up several hundred dollars more in property taxes per year no matter what part of the state I picked. Also Ohio uses city income taxes and not personal property taxes, where as NC uses personal property taxes instead of city income taxes. Actually due to the closeness to the ocean I'm actually surprised out property taxes aren't higher than they are.

I do think in larger cities public transportation is becoming more acceptable in more areas of the country. Not sure how to make more acceptable in small cities where there aren't the businesses and the vast number of jobs in fairly small areas to make it really even viable. Or in a case like where we are when the military and fed govt (civil service jobs and also contractor jobs all on base) accounts for at least three fourths of the jobs for the city how it would even really be viable when the base will not allow it on base due to security issues.