I genuinely can't tell if you are trolling me, so I'll assume the questions are genuine.
See for yourself. You can grep the jQuery codebase for their browser workarounds (denoted by “// Support:”).
curl -L https://code.jquery.com/jquery-git2.js | grep -A 5 -n Support:
As for Bootstrap, they support a bunch of browsers, all the way back to IE8 if you really want. Here is a list of the bugs currently impacting them.
For me, this means one less thing to have to think about. I really don't enjoy testing my CSS on multiple versions of older browsers, and Bootstrap gives me some degree of confidence that things will work.
Of course not, but I often see you knocking various libraries, frameworks and apps very loudly and very vocally for no better reason than you don't like them. Oftentimes (as is, for example, the case with JSFiddle) you have simply failed to comprehend the use case for said technology. I'm just trying to put the other side of the argument.