What makes you think we do?
In any case, there is some justification for an analyser of government policy that isn't subject to the tides of political fortune the way the HoC is. The lords fulfil that function and have fairly often done a very good job of it, stalling poor legislation proposed by a HoC swept up in a particular 'craze'. A monarchy is as good a way of doing that as any. In fact, any way is good,
except by election because the one thing you don't want is for the analyzer to become just another HoC. This is where the American system gets it wrong - too often the Senate and the HoR are just clones of each other, so they actually just endorse each other which is no use to anyone.
You don't want the analyser to be able to propose legislation, that has to be at the will of the at least notional majority. But you want the arbiter of policy to be objective, not simply another slave to public whim.
That is unless you believe that by definition a democratic system is infallible. In which case I have a bridge I'd like to sell you.