No you are just putting up a selected list of attributes:
Does the prospective Lord possess a Hector or not?
And where does he put Hector?
And what is his/her skin colour?
What school and university were attended?
It's very er, biological for someone who is going to be a Lord spiritual don't you think?
You were the one who raised the issue of the Lords being representative of society:
'what is optimal is the representation of peoples lives at the highest level.' (your quote)
What I have used are the standard demographic measures, which are routinely used to determine whether one group might be representative of broader society, namely:
Gender (over 90% male)
Race (over 90% white)
Sexuality (100% heterosexual)
Religion (100% CofE)
Measure of elitism/privilege (vast majority private school and/or Oxbridge educated)
I haven't include the other 2 standard ones, namely:
Age (Bishops are a hugely narrow demographic, all are in late 50s/early mid 60s)
Disability (no idea)
The Lords Spiritual do not 'look' like broader society, they do not represent broader society (they don't even represent broader christian society) and broader society doesn't want them there.