The number of sites that don't work without 3rd party cookies enabled is very small and from my point of view they are plain broken.
But the bottom line is, despite Safari already doing this, Mozilla was met with a lot of hostility when they tried to implement it, and eventually gave up.
Here's an excerpt from Computer world, that'll give you an idea about how things were unrolling back then.
Mozilla has effectively postponed Firefox's controversial third-party cookie-blocking policy for several months.
...
Months ago, when Mozilla's proposal appeared set to debut in Firefox 22, several online advertising groups, including the Interactive Advertising Bureau (IAB) and Association of National Advertisers (ANA), vehemently objected, claiming that the on-by-default blocking would "disenfranchise every single Internet user" and result in the shuttering of small businesses and small websites. An official with the ANA promised that Firefox users would see more ads, not fewer, if the feature was switched on.
http://www.computerworld.com/article/2498038/data-privacy/mo...
Suddenly they were met with headlines like "Mozilla/Firefox hates small business owners" and they are simply not capable of handling a publicity attack (remember the whole CEO thing?) and they caved in.