So, we arrived in Florence and went immediately to the TI to purchase our Firenze cards for 3 of the four of us (my youngest son is only 16 and so did not need one). The woman at the counter was very friendly , and when said something along the lines of, "For you, the price has just gone up", I thought she way just joshing around with me. But no - as of June 1, the price has increased from 72 Euros to 84 Euros. The date of our purchase - June 1st!!!
Since I had planned on purchasing the card and therefore not made any reservations in advance , UI really had no choice but to go ahead and purchase it. Making matters even worse, we were in Florence over the first weekend of the month, so one of the days in which I might have used the card, it was not used because the museums were free.
We ended up going to the Accademia, Medici Chapel, Ufizzi, Pitti Palace/Boboli Gardens (this was the free one), and Brancacci Chapel. I have no idea as to whether they have raised regular admission prices for the museums at the same time, but based on the prices in Rick's 2018 book, we would have only spent 62 euros to visit those sights (factoring in the free day). Obviously, there is the reduced hassle factor of using the card, but still with three cards, we ended up paying a total of 66 euros more by getting the card - a not insignificant amount. If we had needed to pay for both the Pitti Palace and Boboli Gardens, it would have cost us 85 euros, but if I had to pay, I might not have chosen to pay the extra 10 euros to visit the Boboli Gardens.
So that is something to be aware of.
As a aside, I have to say that all four of us really liked the Pitti Palace and frankly, overall we preferred the paintings that we saw there to the Ufuzzi (though I must confess the thrill of seeing the Botticelli Birth of Venus right in front of me when at the Ufizzi).