The level experience is what is known as the city level at the top left of the screen.
When you grow very fast
- you see more raw materials
- more commercial buildings open up
- you can make more elaborate products.
This means that to improve houses, the products you order are more varied. But in addition, the products that are "uncovered" as you advance in the city level are more expensive, with the consequent increase in the price of everything in general.
An added disadvantage is that if it is not accompanied by an adequately sized storage, it can be very complicated to perform certain tasks.
On top of that, the Contest of Mayors becomes very complicated, as you are always competing with Mayors of the same city level, but who are probably more prepared.
So, in short, growing in city experience level is not as important as it may seem at first.