Initiated by a discussion elsewhare I'm going to admit something: I'm a royalist. I am also a parliamentarian, but I continue to believe that having a hereditary head of state is a sensible thing and beneficial to the UK. I don't want the position to ever become elected.
Why? Because elected heads of state are totally political operatives, from the disaster of Trump in the USA to Sarkozy in France † being jailed for corruption, and whilst the Tories are clearly corruptly dealing millions to their buddies just imagine how much worse they'd be if they had even more power. So, no thanks. And whilst some countries, like Ireland, have a nominally independent head of state, I don't believe that is possible here; the right -v- left axis has become just too extreme.
I was also in favour of hereditary peers for a similar reason. If you have to get elected then you have to curry favour, raise lots of money, make 'friends' via promises of paybacks. By being hereditary, no matter that you may be 'left', 'right', or 'crossbench', nobody has to guess who you owe favours too, you and your vote can't be held to ransom in the same was as a politician who needs regular re-election (and, lets face it, American senators are regularly the worst in this respect; 'pork barrel politics' etc.)
My personal preference for the upper house would be taking a wider range of people with skills and experience which would be useful to the country. Make a list of them and randomly choose 100 to serve for a fixed, non-renewable twelve year term every two years (yes, the current 800 is ridiculous. 600 would be a start on reducing that). If people don't have to lie to get elected they're going to be more truthful about where they stand on matters. Indeed most people aren't solely 'of the left' or 'of the right', they share beliefs across the spectrum so currently (without the multitude of options which would be available if we had PR) they have to choose a Party (capital P) who they dislike least to vote for.