Actually, it pretty much is. That is one of the key ways in which sites gain audience, and it's a huge topic of concern among website creators, owners, and programmers.
Shares drive traffic, and both the website owner and the social network want you to ask yourself on each shareable page, "Is this something worth sharing?" Some people will say yes and that's a win for everyone.
You can say the on-site button doesn't do anything, but it really does. It sends a signal: Other people think this content is worth sharing, you might think so too.
There are other models for sharing content, for example a site only needs a few self-interested posters on HN or Reddit to get traction there, then the voting system and "front page effect" take over. But for a decentralized social site like Facebook, you need a good number of seed posters to decide, "It might be in my self-interest to share this." That only happens with prompting.
Unfortunately, your solution of enabling the user to install an add-on is not tenable for the vast number of users who don't even realise what a "browser" is. Apple's Mobile Safari solution works because it makes sharing simple and frictionless for the majority.
http://www.currybet.net/cbet_blog/2012/05/give-share-buttons...
Good luck with that approach.
An alternative approach is to show users how they are being treated like push-button monkeys. All it takes is some users who are not willing to tolerate it who demand better treatment; then other users see they are not having to deal with the same crap and they demand the same treatment. And then, like magic, web developers change their tune, almost like... push-button monkeys.
It's truly magical.
The solution is not for browser makers to host the share buttons, but for content creators to stop treating users like push-button monkeys and realise that if I want to share it on facebook I'll do that of my own volition and if I don't then a little blue and white f in a box at a cute angle is not going to sway me one iota.
Web page creators: It is not your job to make sharing easier.