If it was only one bishop the principle is exactly similar, no group or any one person should be having a privileged position there in the house, including those of us that are all for the secular standpoint, ie., no privileges for any person or group of people no matter what they happen to believe.
There is no privilege in terms of having Lords spiritual and Lords temporal. That should be blindingly obvious. That's the way it is constituted. whether the composition of the Lords Spiritual is within the original spirit of the establishment is I grant you less clear.
It is a house of privilege in that Lords are recommended and appointed in different ways. We know there is a bias towards certain groups in the Lords Temporal and I have already posted a link which outlines where privilege exists in the Lords Temporal.
Given that the HOL is not electoral representation. We cannot argue about it along electoral representational lines.
As it happens many aspects of temporal life are not represented. I have therefore no representation from the many Lords who are ex civil servants or theatrical Lords similarly someone with an apprenticeship is hardly represented by academic lords.
The house of Lords positively notionally represents aspects of our national lives and is a notionally oversight and advisory organisation.
Practically the Lords spiritual only comprises 3.3% of total Lords. Easily overruled and leaves a mere suggestive voice.
Given all of that the nature of the HOL is overwhelmingly secular and any further demands are IMV a manifestation of OCD.