I mean, it fundamentally doesn't make sense as an emergency measure and the DB would be idiots not to see that. "We're facing an exceptionally dangerous foe in a month or two and so we're going to start systematically testing our broader population for Sovereign exaltation, creating, already within a few years a class of exalts that will significantly outnumber you. Yes none of these exalts will arrive on time to meaningfully help us fight this threat."
Managing cultural/individual expectations has already been a very significant part of managing this civ and our council, and we've been told this would be a worry of our DB's, so it seems a bit cavalier to dismiss this downside? Especially given that there is at least an opportunity cost (and quite possibly a very real cost) to be paid for starting to exalt Sovereigns before properly installing the Fount.