'Reapers destroy the Milky Way side of any QEC bridge' would be valid, considering that most of the places a QEC bridge would be placed are overrun by the Reapers. Even if you think the Reapers wouldn't, and would prefer to capture them, the Milky Way defenders could be justified in destroying them before the Reapers threaten to capture them.
Either way, a QEC would be easily justified as being destroyed in the chaos of the Milky Way conflict.
And that's if there was one at all- a QEC between an Ark and the presumably dying Milky Way wouldn't be worth much. You'd actually be expecting the Milky Way end to be defunct before you even arrived in Andromeda. The Milky Way won't be sending timely assistance at any point, but another Arc could conceivably coordinate movement and forces for support.
I said it would be placed in the middle of nowhere. I.e. in the space between stars like the Crucible or the Geth base in ME2. The Reapers would never find it even if they were looking for it. It took the Rachni centuries of dedicated searching to find the Mu relay and they had some idea of where it was. The Reapers don't even know to look for it and it could literally be anywhere with the known MW. To leave it on a planet subject to reaper invasion would be colossally stupid. That's like building the Crucible in orbit of Eden Prime.
I would definitely want a QEC installed. There is no reason it would be defunct. Again, that isn't relevant. The pairs are still entangled. As long as the particles exist they can be used for comms. The comms tech can be replaced/repaired. I think they are just going to ignore QEC's altogether. Which will be interesting considering there is no FTL network in Andromeda for the newly arrived to use. Hmm, will see how they gloss over that...