It's one thing to build a building on land that you own. Universities do commonly build new residences, academic buildings, stadiums, etc. Why it didn't happen in your town idk.

Public transit projects take forever because:

1. They don't own all the land. They have to figure out who to buy it from and that is complicated.
2. Safety. You need to know that the system you build will be safe, and when you have heavy vehicles moving at high speed, that means lots of engineering time.
3. Regulations and procedures - there are prescribed processes that public projects need to follow for bidding, selection, design reviews, etc. These exist to ensure safety, prevent corruption, and things like this. But they take a long time.
4. Politics. You can't just pick the technical best option and do it. You also have to sell it to all the local voters, and get legislative approval for the budget. And no matter what you choose, people will constantly be talking about how it's a terrible idea and too expensive, etc.

And probably a lot of other reasons I can't think of right now.