Of course, this logic has several flaws. First of which is the base assumption that synthetic life will inevitably destroy organic life.
Eventually, conflict is inevitable.
Competition and expansion will see to that.
Your reasoning assumes that expansion will be an important motivator. That may not necessarily be the case, but even if it is, like said, it only leads to conflict of interests. Conflict of interest does not equate to violent conflict; there are other solutions, such as symbiotic relationship, co-operation, forming alliances etc.
Even in a situation where the conflict cannot be resolved with non-violent solutions, escalation to violent conflict does not necessarily equate to definite victory of one side - that usually requires that the winning side has some significant advantage in numbers, resources or technological level. And, even then, this does not necessarily mean that the losing party would be completely exterminated.
And, finally, even if the losing party were to be exterminated, this doesn't necessarily mean it is a bad thing. Takeovers of ecological lockers happen all the time in evolutionary history. What the Reapers are doing is forcing their own perception of "good" on the evolution of galactic civilizations by assigning an arbitrary technological advancement level on organic life; when a civilization reaches a certain level of advancement, they are destroyed.
This is not "protecting" organic life from synthetic life; it's meddling in the natural process of evolution.
If the natural process tends to lead to synthetic life taking over and rendering organic life obsolete, then so be it. Why is this a bad thing? No one ever said why the Reapers seem so convinced about that. If synthetic life takes over the ecologic locker in the galaxy and renders organic life obsolete, then it is just one step in the natural process of evolution and nothing to really fuss over - it would be analogous to fish taking over from crustaceans, or dinosaurs becoming supreme land animals over amphibians and earlier reptiles.
If the Reapers are worried about loss of variety of life, they need not be - at some point, synthetic life forms occupying the galaxy will start to exhibit just as much variation as organic life; they will have their own cultures, factions, wars and diplomacy.
There's nothing significant that would make synthetic life somehow less valuable than organic life. To say otherwise requires placing some inherent value on organic life as opposed to synthetic, and it's hard to do that when there's not even a clear definition what life is, nevermind differences between synthetic and organic life.
Obviously each species and culture have a right to fight for their survival, but the Reapers really have no place acting as the Evolution Police of the galaxy, and with any sort of logical processing they would realize this.
This is why I think their motivation as portrayed in ME3 is not exactly ideal, and I would love to think that there is more to them than that.
For example, maybe they are simply obsessed by archiving successful species' genetics and behavioural patterns on a certain time period.
Perhaps they simply value variety of life, and wish to see continuous stream of new species forming new cultures, as opposed to hegemonic structures stifling everything else, like the Prothean culture seems to have done.
Or maybe they have some goal of their own that requires harvesting successful species and creating Reapers based on them. It might not even be necessary to reveal that.
Maybe the Citadel AI could be a VI instead, and when asked WHY the reapers need to convert organic life to Reapers it could answer "No data available".
I always loved that response from Legion when he didn't really know what to say.
