A week back (if I remember right), I had quoted Swami Desikan and how the school has opined of Rudra/Paramashiva (at least traditional ones, laity and newer adherents can be discounted on the basis of ignorance)
Was rehashing while writing a while back and something came up.
Swami Desikan during the course of his commentary on IshAvAsya upaniShat, quotes harivamSha's bhaviShyatparva and in particular Paramashiva's statement.
What's of interest is how he refers to Rudra here
"आह च सवज्ञः" (cf सर्वज्ञ्னான रुद्रன் தானே சொன்னானிறே)
To understand where the school has placed Rudra and the rest of thema needs to take a holistic look at things, however long-winding/boring it might sound.
To throw an anecdote*, a question placed to bhaTTaparAshara was - "how does a shrIvaiShNava treat devatAntaras"
Now, bhaTTaparAshara opens his response with an interesting shift of focus - "Ask it thus. How would devatAntaras treat a shrIvaiShNava".
At the outset, historically, this has sounded high-handed to most I've seen but the nuance gets an answer in another Vedantacharya.
Yes, prasa~NgAt, the term Vedantacharya in the SV tradition has been given to three individuals - shrImannArAyaNa, bhaTTaparAshara, and Swami Desikan. One of those reasons why some of us prefer not to use it when referring to Swami, given its non-unique nature.
Getting back, where does the answer lie?
To quote Swami Desikan from his Daya shatakam,
vishvAcAryAH vidhishivamukhAH svAdhikAroparuddhAH
Jivas in Brahma-Rudra-Indra statures are not there just because they wished to, but are the fruit of their earlier tapas shakti.
"These jivas that have attained the stature of being AcAryas in their own right to the world in entire" [nuances aside]
While at it, for some shameless plug; my defunct blog that seemingly no Iyengar has interest in, so yeah.
In such a condition, bhaTTaparAshara says, the devatAs wish to be associated with a prapanna/shrIvaiShNava, and by the association wish to work their way out faster than their bound duties would allow them to.
Not a derogation, or disparaging. Au contraire in the right.
Now, the only discomfort a non-vaiShNava would have is to see paramashiva/rudra being called a jIva but that's a thing for a different discussion - a certain something not unique to this school either.
Where the laity misses things out in broad daylight is this nuance that puts the likes of rudra at an elevated position. And in essence, the treatment they end up with, to said devatas.
To put a simple thumb rule - no dUShaNa, no bhUShaNa [read upAsana] either.
The root, imo of all this is the kind of rigid binaries we have come to operate on, and blanket application of terms/practices. One of those reasons why I often poke at the usage of the term Iyengar as if it were free candies distributed.
Insofar as the entire treatment goes, one who is a prapanna, is expected to keep away from any devatAs (and preferably even from asking anything to shrImannArAyaNa to be right) but a militant reject has never been mandated. Beside random incidents painted wrong of course.