"Fairness" being seen as the same as to majority > all would just result in what we've seen happen with our democracy experiments in places like the Mideast. The majority group just ends up using democracy as a cudgel against minority groups. Those minority groups of course don't just stand idly by and next thing you know the entire system is in meltdown and beelining right towards the next iron fist.
But in general this cost pales in comparison to the alternative system where by merit of having a simple majority, a majority group can impose their every whim and desire on the every minority group with absolutely no restraint. If you can solve both problems in some way, do feel free to share - and not only here. You'd have solved a core problem of political science!
Yes, they can, especially where the combination of FPTP with gerrymandered districts, unequal allocation (by population) of seats (in all three of the Senate and, because of granularity limits, the House and, as a consequence of both of those, in the Electoral College) makes it possible for a minority with the right geographic distribution to have majority control of political institutions.