Many of us would need the unmodified one to have a working SIM because a lot of those providers require SMS in their auth flow. Expensive for many of us. For me it'll mean I have to do these things on a computer. Until they come for that one too of course.
Don't they usually SMS you a TOTP code that you could then just type into the unmodified one? I've seen some apps that snoop on your SMS to automatically grab the TOTP code but I've never come across one that wouldn't let you manually type it in.
Do you mean you have the same esim on both phones but normally activated on the burner phone except when you need it on the unmodified one w/o access to burner phone?
I can have multiple free esims with my operator. Since I have my auth-phone in airplane most of the time, I don't care about two ringing phones (or the small privacy caveat that comes with sharing the same phone number across multiple devices).