Upstart browsers are not in the position to tell websites what to do; they will just throw up a "your browser is not supported" banner and forget about you. That was where Chrome was in its early days (you were supposed to be using IE 6), and that's where Firefox is now.
We never let economics solve this problem, because nobody pays for web browsers with money. If there was a $10 "sorry, The New York Times violates standards so we don't support it" and a $100 "we'll work around any bug large or small to make it work for our customer" browser sites would be spending money to let the $10-browser-owners see their ads. But, every browser is run as a charity, so nobody gets to pay the actual costs of the workarounds (except maybe in terms of more security vulnerabilities, higher RAM usage, etc.)
I'm not saying this is good or bad, it's just how it is. Browsers are free and will be blacklisted by sites that don't like how they behave. So the incentive for browsers is to do what the sites want, rather than to strictly conform to standards. Shrug.