That's how I looked at it too after this game but...logically it doesn't make any sense for machines to be Reaping flesh if they are eternal, view as inferrior and they have always had existed. Everything about their actions is contradictory after ME2.
But they weren't using flesh, they were using a paste of raw genetic material. Essentially, genetic material is just the organic way of carrying information. So with that in mind, it seams far more likely that they were after the information contained in human DNA and as much of it as possible.
The Reapers didn't have Stealth or Cloak.
Really? A ship that large creeping around and nobody spotted it on sensors until they actually saw the thing land on Eden Prime? I'd call that pretty damn stealthy. As for a cloaking system; that's a bit of a straw man argument as the only one we know about is the one used by infiltrators (i.e. people) not ships.
The Reapers didn't have Asari abilities
The Reapers didn't have Normandy's powerful Turian canon that broke the back of a vessel that was 20 times larger and powerful.
You mean this thing
? It's based
on Sovereign's weapon. You know, the one that cut Alliance cruisers in half like they were made of paper?
As for having "Asari abilities"; for one thing, biotic abilities are the result of a body exposed to element zero and have little nodules of the stuff throughout it's nervous system. What it basically mean is the body becomes a mass effect field generator, like the ones that power shields, fire projectiles and propel ships. So yes, Reapers DO have "Asari abilities."