Why do they care? Why is one (unsupported by any examples and thematically contradictory) doomsday scenario any more likely, any more worthy of concern, any more deserving of a crazy convoluted cyclical genocide plan?
Why do they care if an artificial-in-origin form of life becomes dominant in the galaxy?
I'd imagine organics would care, and the reaper cycle must have originated from organics, so I don't see how that's a problem. Like I've mentioned previously, the logic is similar to that of a conservation biologist, culling aggressive and dominating species to preserve overall genetic diversity with the ultimate goal of maintaining life. Synthetic life from previous cycles doesn't seem to exist in the "present" cycle, so you would imagine that the reapers destroy them as well once they're finished with organics. Assuming this, sovereign working with the geth in ME1 isn't as much of a plothole as many would think. If you can use some of your enemies to wipe out the rest of them, why not? gives you less work to do.
I definitely think that the ending should have been clearer. A big infodump isn't a particularly exciting way to end a story but I think a little more information at the end would have been nice (also, the synthesis ending was a terrible idea and should never have made it past pre-production). Despite this though I don't see the multitude of problems that everyone else seems to be talking about in the logic of the reapers.