"If we have nothing to hide,"

Right to privacy. Even people with nothing to hide don't like being monitored.

I don't see how it would help in your situation either. "Lots of stamps" is annoying to passport control regardless of any other factors (just because you're not a listed criminal doesn't mean you aren't up to something), and I don't feel like the detainment time is going away anytimes soon for these kinds of things. Even if the information is easily accessed, you have to wait for the decision-maker to spare some time to consider the info and give you the OK.