It’s not quite that simple. Your phone has the hardware to connect to a mobile network, but a SIM, wherever eSIM or physical, has the password to get on to the particular provider’s network. My phone had the hardware to connect to Verizon, T-Mobile or AT&T, but the SIM gives it the password to get on to T-Mobile.
Most notably you need to have an internet connection to download an eSIM - so even if the carrier gave them away for free you would need someone with a working phone to help setup the eSIMs.