The only thing I hate more then tying myself down to a fixed schedule is waiting in line. In cities with a high number of tourists advance booking is often a necessity. You may think getting to the site early will let you avoid booking in advance. The problem is many other tourists are having the exact same thought. Unless you are willing to camp out in advance of opening even skipping breakfast may not be early enough.
You may not be convinced so I’ll offer a video example.
The video starts at before 9am. Do you really want to spend your vacation standing in that line? Or would you rather have a leisurely breakfast before waltzing into the museum?
Instead you could go to the official Uffizi website and book your tickets in advance.
Avoid the temptation to buy from third party sellers.
In the end it’s your trip. If you value the freedom of not booking in advance you are free not to. But understand it will likely result in long waits.