I don’t think Florida vaccine requirement law is that onerous. IIRC the law is only about banning vaccine passports. Gov DeSantis is not the type to micromanage how private businesses can operate.
A vaccine passport would make it faster to check vaccine status. To look through vaccine papers issued by pharmacies takes more time. But then people will have to pay additional costs to acquire those vaccine passports.
As I understand it the laws bans business’ from asking a customer his vaccination status, it doesn’t just ban “passports”. Thus cruise lines may not ask a customer if they’ve been vaccinated, thus cannot operate in Florida if they require evidence of vaccination.