1) - Many of the Indoril Hierarchy committed suicide, as well as the Grand Council be assassinated via the Morag Tong. This left Indoril very weak and ultimately almost leaderless.
2) - Hlaalu got not only the Grand Councilor position but also would gain many benefits from the Empire such as Blind eye (Caldera can be seen as a recent example) to their activities, an increase in power and of course having the backing of the Empire in general.
3) - Indoril was reduced vastly in political power both as a Great House and likely a regional power surrounding Almalexia. (As now for centuries the Kings of Morrowind would be of the Hlaalu House. Though I don't know if there were Indoril-Kings or Kings from other Houses. I suppose it is implied that the other Kings were, indeed, from Indoril as a way for Beth to at least describe how far House Indoril has fallen)
This now gives us a few questions.
#1: We know (likely due to an error or Beth clearly didn't want to call the Armor something else) that Ordinators wear an armor in respects to Nerevar Indoril. However, could this armor be also related to some more traditional wearings of the House of Indoril itself? Two Saints of the Tribunal Temple (Olms and Delyn) could have been connected with House Indoril. We know at least Delyn was - and authored many discourses on Temple law and practice. Olms is an 'iffy' as the "Lives of the Saints" does not describe him as such - but one can hold assumptions. As the Ordinator Order(s) and House Indoril 'seem' to have a close bond.
#2: Would there be a difference between what is the Indoril Hierarchy and the Temple Hierarchy? As seen in 'On Morrowind'
The Temple hierarchy more skillfully managed their loss of face, remaining aloof from political struggles, and earning the good will of the people by concentrating on their economic, educational, and spiritual welfare.
The same book of course describes many Indoril nobles and those of the hierarchy comitting suicide than accepting the Armistice. Can we assume that either the Temple Hierarchy and Indoril Hierarchy have molded into a rather definite hierarchy where one can not distinquish an Indoril from a Temple Master or would there still be an almost secret despisal for Vehk's decision (and the Temple's allowing) to go into the Armistice?
#3: Can one also assume that in the Fourth Era, one can still say; "There will always be a Temple if there is an Indoril infront of it"? (Which is more or less a quote for truth on my part. As Redoran, one of my favorite houses, takes the Temple more practically and less dogmatically than their pious Indoril cousins)