When did the Ark project start?When did it all happen?How did it happen under our noses during the 3 previous games?
A project like like would take years and years and years to be implemented,it's a huge project.While we were playing ME1-3 and knew the Reapers were coming, the rest of the races had to learn it the hard way only at the very last minute.The whole Ark theory requires preparation, when did that happen?
I mean, the premise is interesting but they would have a LOT of explaining to do and it needs very good writing to get the stor to make sense.
We told the Council about Sovereign on Eden Prime, and when we met it again on Virmire.
The turian councilor was dismissive all throughout the trilogy, but I totally wouldn't put it past the asari to organise an ark contingency once they learned what happened to the Protheans. They hid the existence of the Prothean VI on Thessia for millennia.
As for secrecy, there are things that are "need-to-know". Shepard isn't even the most senior person in the Alliance, never mind the Council or the galaxy. As people have said there are plenty of reasons why they wouldn't be told about it, including not wanting to undermine the war effort.
An ark would only be used in the absolute worst case scenario, when all hope was lost and the extinction of every species was assured. For that reason, it would have to be the most secret thing in the galaxy. It's the ultimate back-up plan, and if it failed there wouldn't be any others.
The asari councilor even obliquely hints at something like an ark after Thessia, when she says she would need to put plans in motion to ensure the preservation of civilisation. They could easily use that one line as a way to introduce a secret asari ark project that is opened to some representatives of the other races.