My Telecom Italia SIM ran out of roaming data while I was in Switzerland, and there was no way to top up. Swype had a first month free promo, so I signed up from my Airbnb. I did have to send a photo of my documents, but the total time from download to data was less than 30m.
I took a quick (1 week) work trip to Germany this summer. I was trying to figure out how to get a SIM before getting on the train, when I remembered I still had the eSIM in my phone. I downloaded the app and bought data - $15 per month + $3 per day (since I was roaming). Not only was it super convenient, but I had unlimited data with roaming. I don't think even local cards get you that.
For short trips to Europe, I definitely recommend Swype for its convenience.
Didn't the parent ask about not having to show ID to get a SIM card?
I think it's more difficult in Germany than a lot of other countries.