I don’t know why your cellphone can’t do this. For example, It “knows” which towers are around your home. If all the sudden there’s a new one, pop up an alert.

I use Network Cell Info Lite[0] for this purpose.

Sadly, it's only available in the Google/Apple stores (if anyone knows of a similar tool that's available elsewhere, I'd love to hear about it!)

It allows me to locate the "cell towers" I'm connecting to and that are nearby, as well as the devices around me, and will map them for me.

In fact, several years ago, I noted a brand spanking new "cell tower a block or so away (this is in NYC) that appeared to be in the street(!). It stayed there for a couple weeks and then was gone. It sure seemed like it was an IMSI catcher[1].

It's not directly the feature set you suggest, but can certainly be used to identify the towers near you -- and any new ones that might "pop up."

[0] https://play.google.com/store/apps/details?id=com.wilysis.ce...

[1] https://en.wikipedia.org/wiki/IMSI-catcher

Edit: Another comment (https://news.ycombinator.com/item?id=45189302 ) mentioned snoopsnitch (https://github.com/srlabs/snoopsnitch ) and other tools which, apparently can do similar (and more apropos to the topic at hand) things as Network Cell Info Lite.