Why would the dwemer build an entire city around the statue of a snow elf?
Just to protect the Eyes?Seems unlikely as they could have taken them out and transported them to several other of their cities.
Why would they even let the statue of a snow elf stand in their city?

Maybe the early (untransformed) Snow Elves built it there.

Built after the Falmer pushed the Dwemer out of Irkngthand during the War of the Crag. /spitballing.

Oooooh, I like it. Good bit of head-canon/spitballing.