Don't forget that the Reapers are arrogant, they believe they are the perfect state of existence, that every other sentient being is dust compared to them, that nothing compares to them.
As such, Shepard's defeat of Sovereign, but also her/his constant thwarting of their plans is general is a great blow at their pride. The are completely and utterly convinced that they are undefeatable, and they CANNOT acknowledge Shepard's victories, or else their view of the world would shatter. (Sovereigns speech, and Harbinger's in 'Arrival' clearly shows this, they cannot acknowledge a defeat or even the possibility of it)
As such I'm sure they're attacking earth first as a blow in, as you say, anger, they're trying to cover up their previous defeats, mostly to themselves and their fragile egos.
(SPOILER)
They're also not idiots, they do, in a way, acknowledge their greatest threat, and the greatest potential for a new Reaper considering the final events of Mass effect 2.
As such it would not surprise me if they stayed on earth for quite a while, it takes time to bring in the 'crops' alive, after all.