-The Mora
I understand that the Legion is all this ship is and better, but the key problem is that it's bigger and more expensive. Further, you can deploy more Moras than you can deploy Legions I often find in a single battle. The Mora is a lot more accessible, and while you can't really put too fancy stuff on it, you can usually come up with a good package to turn it into a midgame fleet anchor. Just throw heavy armour and reinforced bulkheads on it, put some low-OP weapons and fighters on it, and it'll soak up a fair amount of firepower leaving you to pull back and vent. That's something I should point out for low-tech ships, they love having low OP weapons on them. ANyway, as a mid-game fleet anchor its got its niche, but its very useful in that niche.
-The Lasher
The Lasher is more of a fencer to the Brawlers stubbornness. You're supposed to come in, activate AAF, try and kill the enemy, then back out once the AAF has worn off. As you said before, its brilliant at pursuit, but it's also pretty good at catching out other frigates (When it has Safety Overrides), somewhat good at providing fire support against bigger targets (With all kinetic builds), and in a pinch as a somewhat poor PD boat for when you can't attain either an Omen or a Condor. I often find it's a fun ship to fly with SO, and I get good use out of it vs other frigates, but on the whole it's usefulness falls off as you move to bigger or better ships. Then again, this happens with a lot of ships anyway. Regardless, it's incredibly useful in the early game, and that's its niche.
-The Shrike
As Thaago said before, this isn't actually a destroyer. It's a frigate in destroyer clothes. It's also a lot of mobile than the Hammerhead and Enforcer, and it's very good at 'pouncing' on overloaded enemies with it's burst jets. The problem is the kind of build you can stick on a Shrike is admittedly limited; you practically need to put Sabot pods on the medium missile, and a high-alpha weapon (mining blaster, phase lance or heavy blaster) on the medium energy. This one-two punch sort of build works wonders against just about anything, but it seems like its the only build that syngerises with its ship system. Long Range builds don't work, because the system moves the ship forward and into enemy fire. You can't stick hardened shields and expect it to survive, because it doesn't have the flux for it. Consequently making a generalist build for Shrikes is just not practical, you need to give it a high-alpha damage build, and watch it clip frigates and destroyers, and that's its niche.
I guess the jist of what I'm saying is that a lot of ships in Starsector are very niche in how they work, and work well within that niche. A lot of people like to use aggressive fleets, which is why they like the Lasher and Shrike - both ships profit from an aggressive playstyle, pushing against the enemy at all times and overwhelming the ships so fast that you don't have the shields pressured too much. Further, these ships are often more accessible than their essentially upgraded derivatives the Medusa and Tempest, so they see more use in early game fleets. Some people prefer to have a slower playstyle where they grind down and outlast the enemy, and thus a Mora will enter into their fleets pretty much as soon as they can afford it until they can get a Legion. So while you may not like the ships for your particular playstyle at particular parts of the game, others might like them for their circumstances.