You might not believe in democracy, but this is still a better system than autocracy. Even if you were right (hint: you're not), this is setting a very dangerous precedent than can and will be abused down the line.
Legal requirements are shaped by such "conveniences" all the time. Of course you wouldn't need a driver's license if you could argue with a police officer at a traffic stop that you are qualified to drive, had no DOIs etc. It's a lot easier though to require a driving test and a current license.
Same thing with the vaccination.
> how complicated the testing is or how many health providers and labs there are.
AFAIK, you can actually test blood reactivity to virus protein, proving a positive.
I'm not sure how you would prove that a person actually got vaccinated and it wasn't the case of doctor pouring vaccine down the drain, someone else taking the vaccine instead etc.
And yes, standardizing such testing, as complicated and expensive as it is, across all the relevant labs across the country would be a bureaucratic nightmare.
I'm not going to engage with your bullshit about doctors faking vaccinations.
Fake vaccinations[3], including fake certificates are popular, especially when they are forced. If you want a fake vaccination, I know a guy who knows a guy. Point is - it's not bullshit.
Yes, checking certificates is easier than testing for antibodies. While harder, I still think antibody tests would have less false positives and I most certainly don't think the relative easiness to administer vaccines is a good reason to require everyone to take them, even when they are more immune then those who only got the vaccine.
A friend had an antibody test as he already had covid and didn't want to go for a vaccine. It was no big deal.
[1] https://www.covid.is/sub-categories/travel-to-and-within-ice...
[2] https://www.landlaeknir.is/um-embaettid/greinar/grein/item43...
I don't even know how Iceland's health system is organized. But it would be a good bet that it is light years ahead of the mess of the 52 states plus territories and whatever! Much different story.