Unlocked Android smartphones can be quite affordable these days. If you prefer iOS an unlocked iPhone 5s from eBay or swappa runs ~ $120.

There are apps for making calls, including Skype and Google Voice (free calls to the US). You can make the call via wifi so you don't even need to purchase a sim card, get the phone unlocked from carrier, or worry about which carrier frequencies your phone may be compatible with. Just look for a decent wifi connection. It is fine to keep the phone turned off if you don't need it. The voice quality over wifi/data has also gotten better, too, though you still often get what you pay for.

Purchasing a local sim card usually requires 15+ min and fitting my purchase into regular business hours so a little planning is necessary. VOIP isn't allowed in every single country in the world so a backup or two is a good idea https://nordvpn.com/blog/why-is-skyp...ain-countries/

As far as "many US cell phone networks not working in Europe", that was perhaps true 6/7 years ago but is no longer the case. T-Mobile data roams for free in many European countries. AT&T, Verizon, and Sprint have paid international roaming passes.