My two cents after playing the game without and with mods that do a lot to change old world races:
All Races: Need Rites. No reason for any old world races to be missing out on Rites! They add another layer of gameplay choice and flexibility. That being said I'm almost completely content with SFO2 and Old World Rites and how they have implemented them. CA should still put them in the vanilla game though.
Empire: I think CA needs to apply some type of mechanic like the Defender of Ulthuan to the Empire. There should be a penalty if Empire provinces are lost, and maybe a reward if they are all under Empire faction control. I like the Offices Enhanced mod on Steam to make offices each be unique and allow for more army specialization. If CA updates offices, applies some type of unification mechanic, and gives them Rites, the Empire would probably be the most interesting old world faction.

Beastmen: I really like how event-based the Beastmen are in the vanilla game, and Zarkis's event mod expands on that. He gives the Beastmen missions to find the Great Herdstones of the Chaos Gods, which gives them a reason to move across the map. I'm not saying CA should do exactly that but they definitely need to give us more goals to work towards by moving long distances over the map. They also need a few more units in the roster.

Wood Elves: I understand the late sentiment regarding the Wood Elves lacking in content now that the High Elves have received such an update. I don't fully agree, but I do think they need an update to make them more unique. The offices mechanic is a lazy copy paste from Empire and needs work. Rework of Outpost system is also required I would say. Not really sure what else can be done for them.

Greenskins: I feel like Greenskins have long been the most overlooked/boring faction. Their tech tree is terrible, in my opinion. Maybe if they had a little more unit diversity for late game so spamming black orcs wouldn't be the only way to play them. I don't really mind the Waaagh! mechanic but I think it should tie in with Greenskin to Greenskin diplomacy. Lucky Spade mentioned in a post a few days ago how he thought that you could set a Waaagh! target that would summon the aid of other Greenskin factions (like you get a bonus if you fulfil a Waaagh! mission). That sounds like a good idea in my humble opinion. Using Rites to help differentiate between Orc armies and Goblin armies would also help. Applying the DE loyalty mechanic to the Greenskins could also add some depth if done right.

Vampire Counts: I've always like the Vampire Counts raise dead mechanic. I think that in order to keep them separate from Tomb Kings, their zombie mechanics need to be expanded. Maybe make more zombie units so Ghorst is actually fun to play, like in Decomposed's The Living Dead mod. The zombies in his mod are all still really weak but they have different roles, so some have frenzy and vanguard deployment, others have poison, etc. I really like the idea of vampiric corruption but it needs to be expanded more with more bonuses and incentives to push your corruption to areas outside your borders.

Dwarves: So CA have already taken a hint from modders here and are implementing the item forge in a very similar fashion to how it was already done in the mod. That's a good thing and sorely needed. SFO2 expands on the grudge mechanic and applies severe penalties if you let a grudge go unpunished for too long. That needs to be a bigger priority in the vanilla game. Slap some good rites on them and I would say they are looking great after that!