Cheapest way to get cell service only for public transit

Any reason you can't just use a physical credit card for touch & pay?

If you think you'll rack up a lot of rides, you would want to use the
same card for all trips if there's a daily cap. This would be for your
husband and be a different card than the one stored in your wallet.

As such, the phone is going to use whatever credit card you have stored in your
wallet (Google or Apple). So having an eSim is, I think, not going to make
a difference if two people cannot use the same card.

Also, since the phone uses NFC to communicate with the turnstile to make
a payment, your husband can turn his phone on and just enable NFC and
make the payment using his phone without enabling cellular service.

You can tap and go with a credit card. Or even buy a bunch of paper tickets at any tobacconist shop and stamp them on the machine on board.
Some Italians have no cell phone, including my cousin who refuses to have one after retiring from TIM (the largest mobile phone provider) as a telecommunications tech.

For most tap-to-pay systems, your phone does not need service. I suppose it could be different for transit systems, but I doubt it.(as long as the payment terminal has a connection)

I would try it, have a physical card as back-up.

Buying an esim is a very cheap and easy way to get data access from cellular service without any actual calling or Italian number. This will essentially allow you to act as if you have WiFi everywhere.

I have used Airalo - buying and installing esim from their app because their instructions and support are good. Some people complain they are more expensive than other esim services, but I think they are still cheap - especially compared to the cost of the vacation. I just checked and their 30 days 10GB is $19.00. Buy what you think you'll need and if you run out you can simply top up on the go.

That being said I usually use cards for "tap in" on transport simply because don't always trust my phone to awake and charged and not give me trouble when getting on a bus, but that is a personal preference. Italians certainly love their cell phones.

Have a great trip,
=Tod

Confirming Rome uses NFC, meaning you don't need data access.