I actually rather like the idea that a small part of the Lords should be selected entirely at random.

That's what hereditary basically does

Let me clarify. Randomly selected such that over time they will represent all walks off life, backgrounds, regions, ages, faiths and so on.

Heredity as it is (or rather was) favours white, male (many of the titles couldn't be passed to women), upper class, privately educated, wealthy, christian individuals.