@Mardee -- the rest of the answer was so thoughtfully composed that I figured it must have been a typo, but wanted to point out just in case!
@jules m -- It's true that the principal downside of using a foreign SIM is that it does make direct calls and texts from US numbers more difficult. You will either have a foreign phone number (if you buy a physical SIM) or no phone number (typically if you buy an eSIM, which will only come with data).
This means phone calls definitely will not come through and texts -- specifically, SMS messages -- will not show up either.
iMessage in my experience is hit and go (it has to do with how it's configured it seems, but I've had mixed results). Other messaging services that are truly independent of your phone number -- e.g. Whatsapp, Facebook Messenger, Telegram, Instagram messaging, Line, Twitter -- will all function perfectly fine. And all other apps that are not directly related to your phone number (email, camera, photos, news apps, etc.) will function identically as in the US.
For automated alerts (fraud or authentication-type things) see if it's possible to send to your email in addition or instead. That will sidestep the SMS messaging problem.
Personally -- I'm an iPhone user on Verizon in the US and have converted fully to using eSIMs when traveling abroad, where available. My thought process is that if there's some true emergency that requires me to be fully contactable, I'll be contacted in SOME way (email, Instagram, Facebook, Whatsapp, Twitter, etc.) and I can always switch my Verizon plan back on if necessary.