I love the Doom to pieces but it is absolutely overpowered lol. Phasing is incredibly strong to begin with, and then the Doom has that, generous fitting stats, an incredibly flexible and well-positioned set of hardpoints, and a ship system that is good on its own merits and then also bamboozles the AI into turning its shields in the wrong direction.
With skill and timing most ships are deadly in player hands, but the Doom stands out in particular as being able to solo entire endgame fleets effortlessly and in an extremely repetitive manner -- drop mines, phase out, shoot them behind the shields if they have omnis or poor coverage or just overload them otherwise, phase in, if they didn't die in one volley repeat.
I really like the playstyle that phase ships represent -- this sort of submarine analogue, these silent deadly killers that can flit behind enemy lines and strike to devastating effect. I wouldn't want anything to change that feeling. But right now, they're more like World War I submarines -- there's just no answer to them, which is bad both for balance and also in the sense that after the initial thrill of how powerful they are wears off, flying one becomes rote and boring.
Even worse, the only real specialized counter to phase ships -- the Harbingers's ship system, which can drag them into normal space -- is on a phase ship itself.
I think it's okay for phase ships to continue to be relatively invulnerable when phased out, but the cooldown for returning to phase should be significantly longer, and there should be some way to force ships out of phase pro-actively instead of just kind of stalking them until flux does it naturally. I wouldn't want every ship to be able to do what the Harbinger can do -- it's too binary, going instantly from total invulnerability to "overloaded and helpless" -- but some way to force them to take on additional (soft?) flux when they're hanging out right next to you, like someone suggested earlier, might be good.