They can dely Bills, they have no power of Veto , and this limitation means that even if they have agenda they wont be able to influence the bill that was pushed by polticians in HoC. Lords do not have to be populists because they arent removable.
Prime Minister again is a leader of his party, has party affiliation, has to respond to changes in the Society. Head of State should not be a President of those who voted for him, he should be above such things.
Plus making a PM a head of State would make him de facto electable dictator that completely dominates politics (Monarchy still serves as some sort of symbolic institution above it), especially in british FPP system which favours government. (Look how many bills did Blair loose in House of Commons during his tenure)
Like i said before im all in favour of limiting resources for the royals, if the money is such a big issue.
Of Course there are no such thing as person with unanamous support (such things are only "possible" in totalitarian states", and dissent is what makes democracy work, but symbolic head of state through having limited political power can serve as Uniting figure in moments which are dividing society.
Think of HoL and Monarchy like of Judiciary, they arent elected and democratic thats right, but they make the system work, by providing guidance, rules and expertise. While still having still centre of power responsive to demands of the public in HoL
Quick question
Are you in Favour of Electing let say Judges or Prosecutors?
Or Making Civil Service Electable and Openned to Public Scrutiny?
Having every Official in the Country Electable would create Chaos (imagine if Supreme Court in US would be electable, things like Freedom of Speech, Right to Choose would be endangered)
I am not saying that British System is Perfect, however it is system that have survived Centuries from Magna Carta , through Reform Acts until now.
