I really don't know what's so hard to understand.
Shepard: "If you'd told us sooner, we could have prepared for this."
Vendetta: "It was feared that if the Reapers learned of the catalyst's intended use, they would retake control of it. I was programmed to withold that information until the Crucible was ready."
According to Hackett they finished the crucible by the time you attack Cronos Station (except for the reaper heart/brain, I guess). Yes, maybe the final battle would have taken place in the Serpent Nebula and not in Sol (if we assume the scientists working on the crucible would have somehow activated the beacon without Shepard), and that would have been then only difference.
Tevos explicitly says she was just informed -> Shepards squadmates discuss the beacon when you enter the temple (you can side with Liara or not) -> then we learn that the Cipher was a requirement to activate the beacon -> people stop blaming the asari (let alone Tevos)
The situation isn't even similar to Rannoch or Tuchanka.
Shiala (the
real war asset) plucked off Feros -> Shiala shares the Cipher with any Crucible scientist who needs to read something Prothean -> Dozens of candidates now available to potentially activate the beacon (guaranteed to be an object of study)
Beacon revealed early, just another potentially helpful Prothean artifact -> Beacon removed from Thessia -> Cerberus doesn't capture Vendetta -> TIM doesn't tattle to the Reapers -> Crucible docked with Citadel, war ends without a final climactic space battle.
Yes, maybe certain Matriarchs would have taken a pounding come election season.
Maybe. I suspect the Asari themselves would be far less offended by it than everyone else. Maybe they'd have to deal with some blowback for hoarding Prothean technology while treating anyone else who does so as criminals. Somehow, I suspect the galaxy would have survived it.