Erik Mona said:
The book mentions that demon lords control their layers more or less at will several times. The layers have the "divinely morphic" trait from the MotP, and for these purposes the demon princes who control a layer qualify as "divine."
By the RAW, this means very little (and if it did, it would mean that the CRs are too low to begin with) without further explanation.
Without a clear indication of the demon lord/prince's "divine power," this control could mean something as minor as making it smell like odur all the time and giving everything a greenish tint. Big. Deal. At best, the demon prince can make it unbearably cold or unbearably hot... Which will not do
anything to affect most true demons (balors, mariliths, et. al), much less rival demon lords or gods. The greatest extent of power, the ability to affect magic traits and travel into and out of the Astral Plane and so forth, all requires at least lesser god if not intermediate god power. Hell, a god could just cast Hand of Death and kill the demon prince without even having to enter its realm.
Now, let's assume that there's more to this than Mona is saying and that there are some clear guidelines. This begs two questions... Are the CRs of any value whatsoever with this in mind (NO) and why not just build them in a manner comparable to gods rather than just hand this paltry handmedown?
And getting back to this whole CR thing... While CR was never initially conceived as a comparison between two monsters, it is often a decent indicator of relative power. For example, a solar is both one of the strongest beings in the MM and possesses one of the highest CRs. It can take down virtually any creature with a lower CR (including a tarrasque) and the few creatures strong enough to defeat it possess higher CRs (pretty much just great wyrm dragons with the proper spell selection).
From an internal cosmology and consistency, it stands to reason that a demon lord would not only have a higher CR than a balor, but would also be stronger than the balor. It also stands to reason that if it has the ability to snub it nose at gods, its CR should somehow reflect this.