My girlfriend could keep her home phone line enabled while using the eSIM but I couldn’t, even though we have the same model of phone! Turns out her home line uses a physical sim, but mine is set up using an eSIM and the iPhone 12 can only have 1 eSIM enabled at a time. You can do 1 physical + 1 eSIM, but not 2 esims.
I couldn’t get texts or calls from home without noodling with my phone settings each time. And FaceTime kept enrolling and unenrolling my number.
I would love to turn off my US eSIM when not in use (I think it uses more power connected to two cellular networks) but that would require unenrolling my US iMessage number and I can’t do that. Definitely the most annoying part of the whole thing.
I considered using a spare iPhone to host a physical SIM with my US number because that would allow the number to stay bonded with my Apple ID and potentially forward SMS over iCloud, but I decided not to because in my experience the SMS part is too flaky to be relied on.
It nags you but you don't have to agree to remove the number. I routinely replace my SIM card when traveling outside the EU and my iMessage number still works for green-bubble people. I ignore/refuse the phone's occasional suggestions to "update" the number.
IIRC this is a limitation that only applies to iPhone <=12.
I am pretty sure that newer iPhone models all support dual-active eSIM, irrespective of whether or not you have a physical SIM slot model or not.
(I used the Airalo app. No association. It worked great.)