Assuming it's not secure digital maybe. A digital passport would be really hard to fake. Not that I assume we'd get one cuz freedom and stuff
Digital would probably be easier to hack and fake. The government is one of the worst players when it comes to IT security.
Depending on the system, there's different attack vectors. The problem is, the first line wasn't designed for this. Let's say there's a perfect secure central digital registry, run by some perfect entity with perfect security between the group checking and them. Scan a QR code, they show your picture and the person evaluating decides if that's you. Even if all those things were true, it's still suspect.
We just moved where the fake happens. The process to get an entry into that perfect system still has to determine that someone was vaccinated and create the entry. If they're just taking your word and a scan of the vaccine card you got, they'll load people who faked it. This pretend perfect system will vouch incorrectly that someone is vaccinated, creating legitimacy for the fake.
I've been waiting to get my Global Entry approved for two years. This would be essentially the same program except they'd need to incorporate medical data and process 300 MILLION people. A vaccine passport would take decades at government speeds.
This is the type of process that would be needed. Something like a real passport, where they put some effort into validating the submitted material beyond just taking your word that the documents are valid.
It makes sense when traveling between areas with different responses, like countries. Transitions that already require actual passports. Adding a vaccine passport as an enhancement to a real passport makes sense. Starting to require passports for things that don't already require passports isn't likely.
Florida isn't going to set up entry check points on the highway or use airport customs for domestic travel all of a sudden. Which just means, eventually, the way Florida, Georgia, Alabama, and every other state are responding will find an equilibrium. At the end, we're not going to have a bunch of states under control and others not.
If we're not doing it at the state level, we're certainly not going to do it at a business level.
Cruise ships may be an exception, sort of. Since all cruising in the US involves an international destination, customs and passports are already required. Which means cruise ships can fall back on real passport updates with vaccine information, leveraging the nation state infrastructure.