You're wrong about the F3 random advantage thing. Blocking low against some character's moves, F3 included, causes an input bug. Your character will randomly stand when you let go of block. This is not from trying to jump. You can be holding down for 5 seconds, against 10 F3's..then let go of block to poke and suddenly get a standing attack. That's a huge problem against someone like Cage who can continually pressure you with a neutral mid-hitting move that confirms into the nutpunch. And you can't stand block it because of his frame traps. So this "trying to jump and causing advantage" really isn't the whole pictures as to why F3 is so good.
It's because it's a mid-hitting, neutral on block, 9 frame, combo-nutpunch starter, that causes input bugs when you try to poke out from blocking low,...which you MUST block low because you'll be caught in EX forceball frame traps and low pokes all day.