Why is renting a wifi router much better than using an eSIM?

E-SIMs may seem like an economical solution for having a data connection in Italy and Europe, but you have to deal with the following problems:

Tethering is not allowed
Almost all e-SIMs allow you to use data only on the phone where the eSIM is installed, because tethering is not allowed. This means you have to get more e-SIM if you want to provide a data connection for your entire family.

Using your phone as a router
In the rare cases where e-SIMs allow tethering, only a few connections are permitted. But the real problem is that your phone is not built to perform the function of a router specifically, but only for a few hours in the best cases. The antenna for WiFi transmitting is small and ineffective, and as a phone performs many other functions at the same time, the processes necessary for the usage as a hotspot congest the processor and considerably increase the battery consumption. The effect you have is that the phone becomes very hot, not responsive, and the battery drains after a few hours.

Speed limits
Even if those who provide e-SIMs in Italy and Europe indicate "unlimited", the speed is reduced after a pre-established daily or monthly traffic, per day or month,  often to very low values making your data connection unusable.

Compatibility
At the moment, only a few smartphones allow you to download e-SIMs. Additionally, if your home country is outside Europe, you must check the compatibility of your phone with the frequencies of the operator networks in Italy and Europe.