I'm pretty sure that White Rooms predate Shenhua, so probably aren't compromised.
Uh, as far as I'm aware they're a Cai family thing. With the Cai being third generation cultivators counting Renxiang. They were very likely invented by, or perfected by Shenhua.
Also noting that nobody really remembers what happens inside a White Room.
Looking at the list, I think it may be incomplete. The big things I think it's missing are:
Formations: the White Rooms show us, I think that you can have Cultivation boosting Formations. They're unusually good and in high demand, but I doubt they're unique.
The White Rooms function as Cultivation Sites and we know those can be artificially induced or moved around, at least, for up to Green sites.
Not meaningfully different from simply having cultivation sites, other than the usual of old and powerful clans being able to obtain them more easily.
Talismans: Although we've not seen it, I would expect that the same would be true for Talismans. They're reasonably arbitrary magic.
We've seen it. Suyin's Impurity Magnet is one such.
That we don't see them in more use does point to them being uneconomical for Reds and Yellows in some way, Yrs made a point of noting that if its easy to do and effective, the noble clans would be doing it already.
Based on Suyin's one device, we can speculate that it takes sufficient skill to produce and have limited enough production runs that they're likely bottlenecking on "anyone who could make one has better things to do than make one for Reds".
Might be more common at Green and up however. We'll see
Teaching Focused Arts: A big advantage of a decent sized noble clan is that they're big enough for members to specialise. That mean that you can have some of the elders that have started to stagnate in pure Cultivation terms develop/learn arts that make them very good at helping their juniors Cultivate/channel energy into them/whatever.
We know Bureaucramancers exist. Guiding Moon almost certainly has Enhanced Education arts, Mother Moon likewise for Child Raising Arts. Reasonable conclusion, but I folded all that under Tutors. Good quality tutors are invariably cultivators of significant potency, and thus their time is a rationed Clan Resource.
Incidentally theres likely some Argent Path Inner Sect disciples with Teaching Arts, because they can teach any element, which means that they can take a wide enough range of Tutoring missions for their sect points on a regular basis(and probably find a cultivation art that gives cultivation progress for teaching).
It WOULD certainly be very very lucrative for a newly minted Baron/Viscount to get some of these.
Coaching: adults in Cultivation schools will have both transhuman intellects and social skills as well as the general bonus that comes from having massively superior Cultivation levels. Given that purely mortal parents and teachers can manage this pretty reliably, they should be more than capable of instilling young nobles with phenomenal levels of intrinsic motivation and the other characteristics that make up lower case t talent that it makes Ling Qi look like a disorganised slacker.
Cram Schools: Clans also have scale efficiencies when teaching batches of young Cultivators the same arts.
All these were listed as early tutoring. Their availability is likely lower for pre-teens who get less out of it however.
I'm not sure about cram school efficiencies as much, since it takes a very large clan(or a Sect) to have enough students on a regular basis to make them worthwhile. Noble clans like to space out their kids so they got enough good stuff to go around, while at higher cultivation things become too personalized for such efficiencies to apply well.
However, they WOULD probably be a great way to develop House Guards and artificers for Reds and Yellows to feed the economy.
Blessings: Those noble clans with ancestors descended from Great Spirits should really have a pretty effective inside track about how to attract their blessings for their descendants. We've seen how powerful these can be.
Hadn't really seen any blessings going around, but they're by nature hard to notice.
Lastly, synergies: the older clans have also had thousands of years of trial and error or even active research programs by superhuman intellects to work out how to best combine all these factors for multiple effects. We've recently seen how even the combination of a talisman and a pill is better than each alone, so how much better would all of these factors added together be.
We see this already. Just consider what kind of cultivation bonuses Meizhen gets for:
-A cultivation art which boosts Water(like their built in water based cultivation art we knew she actively suffered in cultivation from until we found a nice lake for snek)
-A cultivation site which boosts Water(like you know, one of their Thousand Lakes)
-An A-class spirit which boosts Water(hi Cui!)
-A spirit bloodline which boosts Water(hi White Snek!)
-Bai specific drugs
A Bai cultivating Water at Yellow could easily progress thrice as fast as anyone else of the same Talent.
But do note that age does not equate to innovations. Most clans are likely going to grow much faster in their first three centuries than their last three millennia, because they'd have found a comfortable and efficient pattern to fall into, and as is human tendency, grows conservative(especially when the Good Old Days codger is still around and powerful)
For example, say that a Ji Rong level talent showed up in a Ducal clan. They'd be crazy to send him to a sect rather than educate him at home during the peak Cultivation years. To be honest though, this should apply to all nobles. They should be coming to the sect in their twenties as Cyans for the equivalent of post-graduate studies. Of course, this is true irrelevant of Cultivation, fourteen year olds are too young and impressionable to be removed from their clan's direct guidance and exposed to the hostile environment of a sect (particularly Imperial sects that are enemies of the nobility, it's just asking for their loyalty to be subverted).
The bolded is the deliberate intent.
And also paints a more antagonistic picture than is reality, since the whole stunt largely seems to go by:
-Low Nobles are attracted to the Sect by the opportunity and ability to tap on resources(particularly arts!) they can't get easily otherwise. They also get a lot of connections above their level. They'd gladly send their best and brightest, because frankly they NEED that advantage.
-Mid Nobles are attracted to the Sect for the purpose of poaching talents amongst the commoners and low nobility, the Sect lets them because it keeps them coming. They also get a lot of networking done with each other. They would be sending a scattering of future leaders to hobnob.
-High Nobles are there as political statement.
--The Imperial Seat supports the Sects, so the high nobility must show at least token support for the Imperial initiative. A branch family member every decade or so maybe?
--However, they cannot send total embarrassments because that'd shame them, whoever they send should comfortably punk the best that the Low Nobles will be sending. Not hard given the resource gap.
--In addition, the more High Nobles are sending the scions to the Sects, the more all the OTHER High Nobles must match the move, to avoid being politically isolated(not too different from the Sun King strategy no?).
--Which means they must start sending actual quality scions because fuck letting rival noble clan get one up on them.
Meizhen should be the typical Ducal scion in Sect setting. She's talented enough to make a good show, she's not popular internally so if she gets 'corrupted' by the Sect's ideas, so be it.
Renxiang is here as a political move...evidently Shenhua supports the idea of the Sects, it actually fits quite well with the Way of her Domain to bring all the diverse clans of the empire in line...but also as a Ducal Clan of two her motivation is ALSO to make sure her heir has her own allies and connections, if she wants the clan to stand after her ascension.
Liling is here as a surprise. Meta wise we know Sun Shao wants her as far away from the bloody jungle as physically possible, and he could hardly send her to another clan for fostering without getting funky looks.
This year is a bit of a game changer. I have to wonder how many clans changed up their Sect candidate after hearing that three ducal scions are showing up this time.