I'm not sure.
He's 3RKOing the weakest enemies in the Prologue, meaning the only person with inferior offense is Ethlin. He has the same attack as Fin, but Fin doubles anything with an Axe and still ties offense vs. Bow users (Noish technically has a slight lead due to his 7% Crit). He does win durability over Fin thanks to WT though.
He probably isn't getting the Pursuit Ring until vs. Zain's group in Ch. 2, and he needs 28 attack to 2RKO the Arch Knights, 29 attack to 2RKO Axe Knights, and 31 for the Lance Knights. With his strongest weapon, the Iron Lance, he'd need to be about Level 15-16 just one round the weakest enemies, and he still wouldn't be doubling with the Pursuit Ring since they have 0AS and he has -3. At more reasonable levels he's borderline vs. the Lance Knights if he uses a Lance since he's got about the same Speed as them. He has C Lances still so he can't steal Fin's Hero Lance (Fin is fast enough that he quads everything save the Troubs, which he 2HKOs anyway). So realistically, he's likely using a Steel Sword and 3HKOing and hoping for a Crit, which is pretty sad when Fin is only ~3HP/~1 Defense behind him and has Prayer.
Cuan also wants the Pursuit Ring until he leaves, as with it Cuan can make full use of the Silver Lance (which no one else has the weapon rank to use) and one round... pretty much everything that has less AS them him. 40 attack is massive, even the strongest armor in Ch. 3 crumples is being 2 shotted by that behemoth. The only things Cuan isn't one rounding with the Pursuit Ring are bosses, that 1 Bow Knight, those 2 Generals, that 1 Bishop, those 3 Sword Armors, and the Cross Knights (They DO attack him with a Sword at melee, right?). Although for the Orgahill section he can sell the Pursuit Ring since he one shots generics with the Gae Bolg.
Levin at Level 13-14 is also getting all the Armors, and lower levels still picks off stuff like Cross Knights while having a good chance of killing anyway with Crits/Continues.
So he has very stiff competition in Cuan in Ch. 3 for the Pursuit Ring, and even with it he falls short of everything Cuan does plus the Armors (he could use the Iron Cutter, but lots of people also want that).
And then Ch. 4 rolls around, and Ch.4 just spits at him, because Ch. 4 enemies are a huge jump in AS. He's not one rounding Pegs. They have like 11AS minimum and he needs like 37 attack to 2HKO, which is, quite frankly, not possible for Noish (even with the Wing Clipper he only has 11.4AS at max level).
Levin isn't 2HKOing either but has Continue and better Crit and actually doubles.
Note that other sword users CAN reach 37 attack. Ayra and Holyn get it at Level 20 with just a Steel Blade, Beo can use a Silver Blade and get it, Sigurd gets it with his Silver Sword, Alec can double with the Wing Clipper, Lachesis can use Bows, etc.
Meaning that Noish not only needs the Pursuit Ring, but he also needs the Hero Sword (which other dudes still want for killing Armors/Bosses/Promos and better hit than Blades).
Wind Mages he needs to be promoted and have the Slim Sword's low low weight for, but other than that they've got shoddy defenses so he's killing 'em, although they hurt a lot.
Lamia's gang is all faster than him (or in the case of the Sleep Sword girls, he's not 2 shotting anyway since they're just as durable as PKs). So he's so slow that most enemies he CAN 2 shot he probably can't even double, and those that are are often too strong for him to kill without a special weapon on top of that.
Ch. 5 is a ton of armors plus some dudes too fast for him plus some mages that base Ayra could've killed with the Steel Blade. But hey, there's some Axe Knights! Oh wait, you need 35 attack to kill those. And Noish at Level 30 barely reaches that with a Defense Sword (12 might vs. Steel's 10). Damn. And that's at max level, too, which he certainly isn't reaching. So he has to get WTD, which gives them easy pickings hitting him... Same with the Arch Knights, only they're fast enough that he can't double them with a Lance anyway. So he *needs* the Hero Sword just to have good offense that are weaker than the Ch. 4 Peg Knights that I already showed everyone else is stomping (Alec has issues now since even with the Steel Lance he has to be like Level 27).
Noish is completely dependent on the Pursuit Ring and Hero Weapons (sometimes both), the former of which is used better by both Levin and Cuan. In the latter case, he isn't the best user of it (as a unit such as Holyn or Ayra or even Alec or Fury one rounds pretty much everything with it meaning Noish is at best tying). Desperation isn't really an argument as to why Noish should get these.