Losing both PFDs, NDs and upper Ecam is more than just a bad day (or night). Was DMC 1 MEL'd? Did just pushing the A/c ESS PB fix the problem or did they have to reset some circuit breakers? Some CBs on the A319 have a memory that have to be depowered for up to 7 minutes to reset the system properly. The standby horizon should last at least 30 minutes. And they did not have a total a/c bus failure because the RAT would have deployed. So the standby bus would have been powered. Its been a couple of years since I have flown the 319/320 but this sounds like another "Oh, it could never happen like that" situation". I had one of those once.
I would have expected that BA Engineering would have checked it out in BUD. The snitch box would have told them what failed but if you do a BITE check and all is well then what can you say but "let 'er fly". A LOT of Sh## on Sparky the Wonderjet has been cleared by doing the Airbus reset - complete power down, go get a coffee and then power back up. Voila - she is fixed!
That's why I fly a Boeing now. (well not really but it sounds good)