You asked: "Why do I have to mail a state tax form if Florida doesn’t have state taxes?"
Read all of this answer, and see if it applies to you.
Florida does not have a state income tax. Only people who have Florida businesses or rental property with tangible personal property have to file a DR-405 with the county property appraiser by April 1.
https://floridarevenue.com/property/Pages/Taxpayers_TangiblePersonalProperty.aspx
and
https://floridarevenue.com/property/Documents/pt114.pdf
If you don't have a Florida business or rental property with such tangible personal property, then you do not have to file a Florida return. You can choose to skip the Florida return, or delete the Florida return before paying and filing if it's not needed.
https://ttlc.intuit.com/questions/1900608-how-do-i-delete-my-state-return-in-turbotax-online
If you've already paid for it and don't need it as explained above, you can talk to TurboTax Customer Support, tell them you didn't need it, and ask for a refund.
FAQ: What is the TurboTax phone number?
https://ttlc.intuit.com/community/using-turbotax/help/what-is-the-turbotax-phone-number/00/25632
