I think you have to make a separation between written language and spoken language. Latin was so dominant as a written language, and some cases spoken, because it was the language of more official circles such as the Church. Another important reason was that Latin was the international language of that time, it was used as the language to speak with people raised in another language, also in Italy.

Another important distinction that you have to make is that Latin, as a written language, could not be used by anyone because not everyone was able to write or read. Spoken language was already much different in these time maybe even for centuries.

In Italy Latin is ofc in many ways the base of the spoken language. It developed into several branches over many centuries. In other words while Latin as a written language survived, the spoken language had already many variations in Italy, it developed from Vulgar Latin for example.

Dante, and other writers, starting to write their work in the Tuscan dialect certainly helped to spread the use of that dialect as the language of choice because of its popularity and that it was more accessible for other readers outside the more official circles.

But it would be wrong to think that the spoken language did not already have a base before, or that written language was used as a spoken language by many citizens, probably, who could not read or write, so.