I've been using eSIMs for the past couple of years for this specific use case, and while they certainly help, it's really just a stop-gap measure:

You still need your phone and cell signal to receive them (at least many European carriers don't support SMS over VoWIFI); the eSIM is "stuck" in your phone if it physically breaks (and on many carriers, you can't re-use an eSIM QR activation code in any case); in many countries, SIMs expire after a couple of months or even weeks of inactivity, losing your number permanently, to name just a few.

I've found Google Voice to work quite well as a workaround for almost all of these problems, but unfortunately, many US companies insist on not allowing VoIP numbers for 2FA or even plain account creation purposes. I usually try to avoid these companies.

I thought I got everything moved over to an authenticator app before leaving home but I forgot one, I got a "check your phone for verification SMS" earlier today. My American SIM could get the text but my foreign sim was giving my laptop internet access. Big pain in the ass.

Eh, I greatly prefer ability to move the very reliable thing from one phone to another, just use another phone instead of going into paperwork to move it if my phone gets damaged or something