How about this; what if all technology eventually developes to the point were species are capable of wiping out the entire galaxy by accident? The only way to solve this is to limit the development of technology to a certain point. The reapers harvest all advanced civilisations every cycle so no species ever becomes advanced enough to threaten the existence of the galaxy, uplifting them to a collective where no of them would have any reason to make war on each other on thus use said weapons. By harvesting in cycles the reapers prevent advanced civilisations from going to war with super weapons capable of destroying the galaxy and thus ensuring the continuation of life. Makes much more sense, right? If they are going to kill themsleves anyway, you might as well do it sooner and stop them from destroying all the younger races in the process. There's a chance that they would not use such weapons if they developed them, but why take that risk when you only need to be wrong once to jeopardise everything.
To hammer the point home, they could explain that the reapers come from another galaxy that was destroyed when they invented the technology, so the survivors fled to ours and decided to do their best to stop the same thing happening here.