You are completely right. Tiebreaks are not the best way to decide who wins, which is why in most important tournaments the winner is decided by a rapid match.
It's a bit crazy...
If you can beat stronger player you are probably stronger player than the one who can't. That's logical.
Yes, but the other guy performed weaker against weaker opposition, too!
As AKAL said, tiebreaking games are usually preferred.
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You are completely right. Tiebreaks are not the best way to decide who wins, which is why in most important tournaments the winner is decided by a rapid match.