Your public IP will be where it exits the carriers' private networks, right?. I learned about roaming in GSM networks long ago, and it at least used to be that all the traffic went through your home network if you're roaming abroad. If that's still the case, it would make sense to have a home IP even if abroad.

I don't believe each cell tower will have its own public IP, because if they did, cellular handover and all the clever stuff going on hidden from the users would be even more complex. Also exposing cell towers to the public internet sounds like a disaster.

You can doubt all you want, but I'm just telling you exactly how it is. I checked it in multiple ip location check services. They gave me an IP that was geolocated to my telco providers city.