Your theory on the Reapers

I think the Milky Way Galaxy is not the only Galaxy the Reapers have access to. Given their incredible technology, I don't think it's beyond reasonable speculation to believe that the Reaper race is capable of using specialized Relays in order to travel to other galaxies. Implying that when the Reapers move back into Dark Space- they may actually continue onto another Galaxy to harvest sentient life instead of 'hibernating' as theorized in game. I see this as a logical presumption. Since given their technological capabilities, it seems inefficient on their behalf to wait for another 'cycle' to occur in the Milky Way while other candidate galaxies are left untouched.
Sovereign's word may give evidence to this: "There is a realm of existence so far beyond your own, you cannot even imagine it.."

As shown with the creation of a Human/Reaper hybrid. The Reapers have taken an interest in humanity- but for reasons still undisclosed. As EDI speculates, they may harvest species in order to fulfill a reproduction role. But this seems unlikely, given the fact that the chance of finding an appropriate species to facilitate reproduction seems slim at best. It is illogical that a hyper-advanced race would gamble their entire reproduction cycle on a very unpredictable vector.

Personally, I believe that the Reapers do not harvest species to reproduce, but rather to enhance and/or weaponize. By using the genetic material of other sentient life to physiologically improve either themselves or other hybrid designs that they use offensively. I draw reasoning of this from Sovereign's words to Shepherd on Virmire: "Rudimentary creatures of blood and flesh. You touch my mind, fumbling in ignorance, incapable of understanding." As it explicitly states, Commander Shepherd (along with all sentient life) is incapable of ever understanding the true intentions of the Reapers. Hinting that the theory of reapers using life to reproduce may be nowhere near the truth.

But if the viewpoint of the Reapers is considered, based on this theory of harvesting life as a mere 'biological enhancement' for their own systems or devices. It is understandable that Sovereign would state that Shepherd is incapable of understanding that he, along with other sentient species (defined as self-aware and capable of abstract thought) are simply objectified within the Reaper mind- As a sentient being is truly incapable of considering itself as a mere potential organic objects or upgrades waiting to be utilized by the Reaper race. This is supported by the effects and virtues instilled by indoctrination- a fully-indoctrinated being completely loses it's sense of self. And simply becomes a tool to the Reaper's whim.
With this in mind, Harbinger's notion of 'Ascension' could be compared to that of a scientist using a bacteria to improve food preservation. The Reapers may believe that they are giving the human race a true purpose within the Reaper race- however insignificant it may seem.

As to why Humans are of importance to the Reapers, I find that clues to this are mentioned by Mordin during his loyalty mission: "Humans useful as test subjects. Genetically diverse. Enables exploration of treatment modalities..... More variable. Peaks and valleys, mutations, adaptions. Far beyond other life... Ignore superficial appearance. Down to genetic code. Biotic abilities, intelligence levels. " I find it intriguing that Humans are considered a highly variable species within the galaxy. And I think Mordin's emphasis on this is being mentioned intentionally. Hinting that the diversity of human genomes may be what makes us of interest to the Reapers. Our genetic variability may be an important factor that makes it beneficial for the Reapers to cultivate. Perhaps offering them better flexibility in hybridization between organic and synthetic tissue. Or maybe other improvements that can fundamentally increase a Reaper's/Reaper asset's capability to cope with or resist threats physiologically, biologically, technologically, or in other possible ways. This, in conclusion, would be part of vital improvements the Reapers would require if they were in conflict- as is theorized below

It seems unrealistically diabolical that the Reapers simply cull sentient life to improve themselves for the sake of it. Despite their hyper-advanced state, which renders natural selection (and therefore evolution) irrelevant - War itself would create and fulfill a state a role of natural selection within the Reaper species- forcing them to find ways to either adapt or enhance. The idea that the Reapers are embroiled within an intergalactic war between either a faction of their own kind- or a completely unknown force, gives reason to their actions. Explaining why they are driven to constantly harvest, in order to increase and enhance their assets. The weapons and defensive abilities that the Reapers use are also worthy to note. Posing the question of why they are so much more advanced than other known civilizations. While it can easily argued this is simply to remain superior when pacifying a spacefaring species- it should be kept in mind that the Reapers must of had a vital reason to produce such powerful weaponry in the first place. Warfare on the level of the Reapers would obviously require massive amounts of resources, and sentient species may hold an important key in the survival and further propagation of the Reaper race.