A friend of mine went through this same scenario while abroad. In his case he actually did have the eSIM on a contract attached to his name, but the issue is that he couldn't get it reissued from abroad for security reasons and/or activating it from abroad wasn't possible (if he could get a Wi-Fi network VPN'd back to the UK it would've probably worked). It was a nightmare to sort out, and I believe he had to ultimately arrange a physical SIM getting delivered to a friend in his home country who then forwarded it to him.

> eSIM seems like it was designed by someone from the US

eSIM was designed by committee to allow carriers more control over switching and/or moving SIMs. Carriers see the ability to easily move a physical SIM outside of their control as a problem. eSIM is the solution, putting them back into the loop and ensuring they can do obnoxious things like charge fees on issuing a (one-time-use!) eSIM QR code (the fee made sense back then as it involved delivery of a physical SIM, but now it's just pure racket).