The idea is that by the time you've finished fighting other enemy ships (while managing the threat from enemy phase ships), the phase ships are already pretty close to exhaustion if not already ticking down. Fleet compositions tend to work towards this, with phase ships being much less likely to be found in smaller fleets. If this "CR battle" thing happens occasionally, it's... not great, but imo acceptable. If it happens frequently - i.e. a large portion of the times you're fighting phase ships - then it's more of a problem.
If you don't mind, this info would be very helpful - how often does this happen for you, and what fleets/fleet compositions are you fighting (and how much/what you're deploying) that leads to this happening?
The primary culprits here are the Afflictor and Shade, in low ship-count battles.
Generally speaking, the worst of this happens in destroyer and frigate level action, in the earlier stages of the game before the carriers take over in earnest. I can usually leverage a win within a couple minutes of contact, and after that the phase ships are the mop up. Fleet composition tends towards having low to mid tech destroyers (cheapness), with frigates all over the place depending on what's ended up available/whoever I've been fighting. Call it maybe 18-25 ships in both fleets combined at the most. Universally, I can designate a relatively speedy frigate with an attack (not eliminate) order on the phase ship(s) and ignore it(them) until the mop up phase, whereupon yakety sax might as well be cued up for the duration of the CR time. This tends towards being another several minutes as Afflictors and Shades tend to bounce far enough out of range while venting/repositioning so as to not be taking CR time while maneuvering during the actual fighting (a solid choice of maneuver and at a remove I can commend the AI), with this only stopping when three or four vessels have managed to surround it such that the only way out is through.
If that was it, and the fight ended there, I wouldn't be nearly as annoyed. On the retreat, if the AI pulled its phase vessel out in time, that's another few minutes down the drain if I choose not to just harass. If there's a freighter or four I want dead, well, that's five minutes of not much about to happen if the phase vessel isn't mothballed since I don't have the overwhelming force needed to simply make the AI abandon battle on contact. Especially if I economize on the vessels I send in, and don't send several for every phase vessel still in the fleet.
To be completely clear, bebopping around with destroyers and frigates is otherwise my favorite part of the game, and encounters with phase ships don't happen often enough to dampen my enthusiasm, especially if I give fighting Tri-Tach a miss. Starsector around that point very definitely nails the feeling of being an independent actor with influence on matters but who's ultimately a small fish in a big pond. While I'm otherwise venting on the subject, I'll take the time to thank you profusely for never putting Hardened Subsystems on these things. That random (infuriating) occurrence is one of the axes I could grind against a certain mod, but that's not on you. Excellent choice there.
Harbingers and Dooms tend to be rare enough that I've only encountered them after I'm rocking capitals and carriers or are supporting an allied fleet with the above. By the time carriers, cruisers, and capitals take over as the primary combatants, fights against comparable fleets tend to last long enough that by the time I'm done hunting other vessels (literally anything but the phase ships, seriously I don't even bother), the phase ships have had enough ships piling on that they've left or malfunctioned into dying. Obviously after the battle's largely over at this stage I can also pile on strike squadrons until the phase vessels die on returning to real space, but that's not a valid tactic during the problem times. Exceptions and limitations apply to retreats, of course, but I can just choose to harass, field an unprofitable overwhelming force to make it retreat, or field nothing as the AI chose to pursue and while I wanted salvage from the primary fight I didn't want to field anything myself. This last response also leads towards a few minutes of web browsing, but it's the price of doing business since you can't just leave the fight as pursuit starts and still have salvage.
I don't have a problem with phase ships' position in battle as harassers to draw attention, or that I occasionally just get a ship nuked by one in the fight (afflictor and heavily engaged capital ship is the major interaction, and the most pressing reason why I never let the AI pilot my valuable non-CV capitals) - that's fair and/or a valid punishment for a misplay. It's at the end of a fight that I have a problem with them.
AI is not that good at kiting. If you are in phase frigate/Hyperion/phase DE yourself, catching anything is trivial.
Scarab can probably catch phase too. Wolf can catch, but will have to do so at least twice (since one Heavy blaster won't kill fast enough).
Player piloted Medusa with character skills usually allows to catch them too. AI does not fully understand your ability to chain skim x3 + insta-melt it with Heavy Blasters when picking to spot to vent.
I've never found phase skimmers to be useful to kill phase ships. In my experience they'll be at incredible range when they choose to vent, and it's not like venting turns off engines. I've had the occasional lucky shot from just beyond the maximum range of something hard hitting with a triple phase skim, but luck is all it is. The occasional lucky shot, which happens with AI controlled vessels too, does not make it worth my time to fight. If I wanted to play a completely luck based game I'd load up a slot machine simulator.
It speaks well of the battle AI. It's also incredibly annoying.
All of above was without SO usage. With SO any frigate/DE + Aurora/Falcon cruisers will likely be fast enough.
Basically, you should not expect to counter phase by just moving in their direction and shooting. Using one of faster ships with mobility system is mandatory (or SO). Or just drown them in fighters, that works too.
Only if your fleet is capable of neither does waiting for CR become main method of fighting phase ships.
Hah, as if. SO frigates are, mostly, fast enough to keep a phase ship away from a fleet and I'll task them to hound phase vessels while the relevant ships fight, but I've never had one catch a phase vessel under any circumstances that I'd want them to - Lasher vs. Doom is a bad match up. An SO with anything larger than a frigate is just pointless. Manually piloted SO ships suffer from the same problem that AI ones do inasmuch as phase ships are effectively uncatchable. Sure, maybe I can cut one off at the map edge and down it if I don't get too close and cause it to clown through me and start kiting the other way before it vents, but then I've got my SO ship away from the fight dealing with one vessel of marginal value. And to be fair, I detest phase ships for being hard to kill after the fight, not because I think they're overpowered (they aren't).
In terms of fighters, it usually takes three to five squadrons with some decent HE missiles to reliably catch a phase ship and down it. Individual bomber squadrons suffer from slow ordnance that usually gets dodged. Dropping multiple strike squadrons on phase ships is a waste during the battle: those vessels don't have that much influence on the outcome. Afterward it just brings the time to delete phase ships down from literally all of their CR timer to the time it takes to kill anything else during the mop up plus however long the phase ship has left on its flux. And by the time I have that amount of strike squadrons to drop on arbitrary targets phase ships aren't as much of an issue anyway.