But if every single human is killed, then humanity is basically no more. Genetic code stored in a giant death machine, with seemingly no hope of being used to reconstitute the race that was obliterated, is no more preservation of that particular species than making furniture preserves trees.
Yes.
Preserve organic life.
Preserve civilizations.
ASCEND humanity.
They don't really care about 'humanity'. To them, it is obsolete and frail - almost literally like insects are to us, really. They'll take records of our civilizations and genetic code so that we're not forgotten about, and they let the 'field' continue to grow with organics so that organic sapient life is never extinguished entirely. Yes, they are rather parasitical. The Reapers are not 'good guys', for sure. Just somewhat understandable.
seemingly no hope of being used to reconstitute the race that was obliterated
I partially doubt that. Yes, humanity as-we-know-it-in-ME-trilogy isn't going to be reconstituted. It can't. It would already be ruined. Even if reconstructions were made, it would never be the exact same thing in every way.
But the Reapers really could possibly, if broken from the cycle and strict beliefs, recreate from matter entities that really resembled humans and maybe even carried largely human thinking and memories. Husks for the Cycle were just troop fodder - but there is room for speculation on what Reapers (really just Old Effin-Powerful Machines) could more positively create with their tech level and databases.
Too bad Synthesis (and even Control) didn't communicate that message too well.