Fees or taxes in Florence and Venice that can only be paid in cash?

Nothing recent, but that is normal. If the hotel allowed you to pay the tax with a credit card, it would cost them about 2% or so transaction fee, maybe more if you have one of those triple reward credit cards. Italians don't like paying taxes (do you?) and since the city expects a certain per diem tax paid to them in EUR, the hotel does not see any reason to kick in that extra 2% on your behalf.

My local authorities will happily allow me to pay my property taxes with a credit card if I add a 2.3% processing fee.

We paid a small city tax per person per night directly to the owner in cash last summer. It was very negligible (about 3€ pp/pd). This was done for the apartments we rented in Venice and Florence through Homeaway and was clearly stated in the homeowner’s rental information. We also filled out some paperwork for the city with the owner when we checked into the apartment.

Thank you. Very reasonable. What about departure tax or fee?

Didn’t encounter anything like that.

We've been asked to pay the per night, per person city taxes in cash in a number of Italian cities, including Florence. They've generally run about 2-4 euros pp, per night.

We've usually been asked to pay the city tax in cash. As someone mentioned, it's because the cc companies take a percentage, which means the hotels end up having to pay the difference on the tax.

I stayed in Rome, Florence and Positano last spring and all the hotel confirmations stated the taxes needed to be paid in cash. However, upon check-out they all gladly accepted my Amex card. Go figure. Flew out of Naples and had no departure taxes.

Are you flying out of one of these cities? That is the only 'departure ' tax I know of and generally it is built into flight ticket. Mexico is only time I had to pay in cash.

It’s called Tassa di Soggiorno, it varies from municipality to municipality (where adopted) and it is usually 1 to 5 euro per person per night depending on type of facility.
The law specifically says that ic can be paid in either cash or card.
If the owner of the establishment tells you that it can be paid only in cash they are lying and if he tells you so it is because he is likely to evade such tax. It is currently the most evaded tax having less than 50% tax compliance. The excuse of the 2% credit card commission is just that, an excuse.

I always wonder where you find these data. Mrs Castelli, a deputy minister, recently declared that in "some cities" the evasion rate is higher than 50%. That's all. Nobody knows how many cities and how many hotels.
How do you know the kind of agreement that every Italian hotel has with its credit card provider?