Well, that's because they're really languages and not dialects! They all derive from Latin, there is no "old Italian" or anything, at some point we decided the Florentine "dialect", having the most literary prestige, would be standard Italian.
Italians only really started speaking Italian in their day-to-day life after the war. It was mostly a written/literary language before that.
Yes, surprisingly few Italian dialects are actually Italian derivatives (maybe only a couple?)
But there are differences between a dialect and a language, we can't say all of those are languages even if most come from Latin.
Italian wikipedia says that officially in Italy there are about 13 recognized languages (not counting Italian, plus French and Slovenian in some parts), and about a dozen main dialects.
In wikipedia you will notice 3 big dialect groups that are just that, groups of many, many dialects that do not qualify as languages.
It's more a difference of how recognized by the community those are, and how unified by grammar, locality and uniqueness. Kind of a gray area for many.
> But there are differences between a dialect and a language, we can't say all of those are languages even if most come from Latin.
That's not really true. There's no scientific reason to say that some varieties are "dialects" and some are "languages". It is purely a political and culture question.
> Well, that's because they're really languages and not dialects!
Indeed they are not strictly dialects of Italian, which followed its own evolution alongside them. I think most of them could still be explained as dialects of Latin, who underwent major "niche differentiation" in the immediate aftermath of the fall of Rome and the rise of barbaric kingdoms.
> [Italian] was mostly a written/literary language before that.
This is a bit of an exaggeration. Clearly, even before the early modern era "Italians" could understand each other. Dante (from Florence) lived in Genoa and Ravenna, and had no need for an interpreter from what we can gather. Ditto the many "Renaissance men" who toured around Italy (Leonardo: Florence->Milan; Raphael and Michelangelo: Florence->Rome; Galileo:Pisa->Padua). This level of interconnection becomes really hard to explain without a high degree of mutual intelligibility.
Dante is a poor example for language proficiency, as he was educated / traveled/ well read. The common person would have a much different lived experience
I have colleagues in India. It's a diverse mesh of regions that vary in about every way. Was explained people grow up with 3 languages, their regional language, a neighboring region's language, a more general language, & then educated folk are taught English. Then in school they were still taking classes for other romantic languages. At an Indian restaurant with one colleague I noticed they would mostly rely on hand gestures. One factor here is that there may often be a language barrier
I've also interacted a bit with Senegalese, which has Wolof as the primary language, then French taught in schools. Many only know Wolof (with French influence weaved in). & the well educated learn to speak English, & how to maintain more European French accent
Italians only really started speaking Italian in their day-to-day life after the war. It was mostly a written/literary language before that.