LinkedIn succeeds because they have ads people actually want to click—virtually everyone needs employment, and generally jobs are far more valuable than anything else advertised online. Any given ad for employment will be many, many, many times more interesting to any given person than any given ad on the internet will be.
Facebook has very little worth selling to a young audience that will never click online ads. Who goes to Facebook to find ways to spend money? It's a social network with little relevance to commercial interests (for end users).
Market-specific businesses will almost always beat out the special interests—facebook would probably get more money selling users to specialized advertising customers on demand, or even getting users to pay to make ads/stupid "features" (Games! Anything involving microtransactions! Bugging me to like things I have no desire to like!) go away.
Speaking of which, how is the model of pay-to-remove-ads not more prevalent? Surely it wouldn't REDUCE profits.