If we disregard the fact that many older but still usable phones don’t support e-sim (which was the original point), what do you mean ”just” download the e-sim?
At least in my country, getting an e-sim is a pretty involved process which requires secure authentication, and specifically in my case that authentication would be gone with the now-broken phone if one didn’t have the foresight to have a backup (which many people do not).
If you have a physical sim, you can move it to almost any (unlocked) mobile phone in existence (at least in Europe) and at most you’ll need the PIN/PUK.
Of course, this goes the other way as well if you drop your phone in the ocean for example, provided you have alternate authentication and a compatible phone, e-sim will have you up and running again much faster.