> people who have never been here can point out the expensive neighborhoods because they are the greener ones

This is normal in many cities.

Trees can mean high status because

(a) you need excess land to have trees.

(b) old wealthy suburbs often have old trees (a massive old oak tree implies something).

(c) single dwelling houses that are near the city often have very old trees due to the age of the location, and can have high value because the location has now become central (due to city outskirt growth).

(d) maintaining trees costs time and money, as mentioned, so that also implies wealth (and status).

Aside: lawns are another status symbol - that is why so many people care about them so much! Think of a huge old English estate with manicured lawns, and why that is a strong symbol of wealth.

Edit: and I should say I love trees and I think they are really worthwhile, independent of any associated status!