There’s one reason to do class quests now: to get a legendary trait, one of seven total per class is only available by finishing the class quests.
I can’t recall what legendary is unlocked by each class. These range from must-have to meh, depending on the state of the game and how you play. Examples:
Minstrel gets Fellowship’s Heart (30 seconds of a super-strong heal going off, excellent to fire off just before you die), which I’ve permanently slotted. Especially useful in raids or 6-man groups, as it’s a group (not raid-wide) heal. Was essential for most Nornuan raid groups (the big Turtle in the Waterworks late in MoM-era) and especially in early SoA 6-man groups for Carn Dum and the Rift. Hasn’t scaled well with the inflated morale pools since launch, but still an essential tool for group healing.
Burglars get stick-and-move (evades open your crit chain now, which basically permanently keeps it open if solo). Much better back when you could get 25% evade as a base, but it synergizes well with touch-n’-go’s 50% evade for 30 seconds when you solo a tough enemy. Mostly useless in groups as the burglar isn’t the main or off-tank class of choice (back when you could get 25% evade, 25% parry back in SoA days plus 50% evade from touch-n’-go, burglars were the supreme off-tanking class to pick up unexpected adds until the guardian could grab aggro, but have a strict, short time limit on how long they can stay alive without heals, unlike guardians).
Champions get Controlled Burn, an improved fervour stance. Nerfed over the years, was best back at the MoM launch where ‘fervour tanking’ really meant controlled burn tanking. You get to B/P/E while getting the DPS of fervour stance; duration has been cut severely, used to last as long as you were in combat.
Captains get In Defense of Middle Earth. +50 to all stats. Again, less good now vs. launch as it hasn’t scaled with level inflation (should be +N for level N of the captain to scale…).
Hunters get Bow of the Righteous: you get power back every bow shot. It’s a super-important legendary for hunters, especially in strength stance, or you will run out of power in no time flat.
Guardians: To The King. Potential FM starter, good damage, never leave home without it.
Loremasters get the Eagle pet. Was best in SoA, now rarely seen due to the introduction of the new pets. Has a chance to rez you if you die and it’s still alive, but only a chance.
Warden/RK: NO CLUE.
tl;dr: it’s worth doing the level 45 class quests for most classes in lotro, and you can just run skirmishes to buy (all of?) the items now, so no excuse not to.
tl;tl;dr;dr: oh god I didn’t have to look any of that up, and I haven’t really played in a year. Shoot me now.