I think you when start telling yourself you need a couple of something is where you run the risk of creating generic events that lose the flavor for the sake of having content.
So if your 4 rough ideas are:
-Recover a Chapter Relic
-Kill a hated notable foe
-Seek an answer to a mysterious question
-Destroy a traitor
You basically end up just name swapping. Which is why I think the Chapter histories can provide unique and different ideas that, at least to players in the know, accurately represents the fluff.
So, for example, Captain Tycho was a big Blood Angels character until GWS decided to kill him off. For Blood Angels, seeking out Tycho's killer and avenging his death is a nice, specific, fluff-backed player goal.
Or for Blood Ravens, finding out which primarch gene stock they hail from. (An off the cuff example since I don't think this question has ever been answered.)
Or for Space Wolves, finding out what happened to Leman Russ. (A really off the cuff example since having a resolution to that would be a pretty major event in the 40k universe.)
Dark Angels is pretty obvious, but in the scope of the game I think it would be pretty reasonable to make their goal the complete elimination/redemption of the Fallen.
Ultramarines might be finding the person who cut Guillman's throat. (Been a long time since I read their lore, not sure if this was resolved or not.)
White Scars might be recovering Jaghatai's spear or jet bike or something. The Iron hands could search for the Hand of Ferrus Manus or something.
You get the gist. If you start mixing and matching all those things, you drift away from actual events in Chapter history to kind of fabricating reasons. (Not saying some of my examples don't also do that, but....)
Otherwise, I think the result doesn't justify the effort. Why have specific chapter quests when, if they're kind of going to be mixed and matched, you can just throw them into the regular event regurgiator like most other events. I'm not saying it doesn't work, it just doesn't strike me as more flavorful than specific, fluff-backed quests. And besides, there's still custom chapters, which could definitely make use of so-called Randomly Generated Chapter quests.
In the end though, if you already have canon chapters with honestly more canon chapter features than any other 40k game made to date....why not go the distance?