The main reasons people use to attack the monarchy are actually the main reasons they are better than elected heads of state.
The main 'complaint' about having a monarch is that they aren't in place based on merit.
A monarch is not elected/selected by an electorate, their skills and suitability are never put to the test - the job is simply their by virtue of birth.
This is also the best argument in favour of having a monarch instead of an elected head of state.
The arrogance of elected leaders is astounding - in the UK for many years our choice of Prime Minister has been between the Labour leader or the Conservative leader. While the winner shows great hubris in explaining the great skill, inteligence etc that they have had to employ in beating their opponent, in truth there is no absolute standard.
Our elected PM, is not elected against some absolute measure, they are simply just slightly better than 'the other one'.
A monarch is fully aware that they have their position simply through an accident of birth - it is certainly up to them how good a monarch they become, but the fact they are monarch is no personal reflection on them.
So while elected leaders pretend they are something special - and end up believing it, and acting on it as if they are all powerful gods - a hereditary or other process of merit-free succession keeps the office holder firmly in their place as the beneficiary of good fortune, a debt that they have then to repay to the people of the state they head.
The UK monarchy have done far more to justify their live styles/wealth than (say) Tony Blair or the Kinnock clan ever have, or ever will do.
The Church of England
Just as an unelected head of state is a good thing to keep the role away from the slugs that would otherwise weasel their way into the role under a guise of supposed 'democracy', so the Church of England has an essential role in England - even for the non-religious. Unfortunately it is a role that is is almost completely failing to perform - however this is not a reason to abandon it, either they must raise their game and fulfil this role, or the people must find a new champion to undertake it.
The role is to remind and ensure that people remember that humanity is right at the top of the tree of life, that we are all created equal, and that we are not ultimately accountable to anyone or anything in this world.
In their words, what we do is by God's will, and it is by God that we are ultimately judged. Not by earthly powers - but whether you believe in God or not, the message is sound.
It is not for any earthly power that people are to be ordered about, their lives controlled, their spirit suppressed. Whether you believe in God or not, this principle needs to be maintained, and the Church of England was the institution that used to maintain it.
With the monarch protecting the people of the UK from big tyrants, and the Church of England protecting us from smaller ones England was a pretty good and free place. But this is being put under pressure by 'presidential' style governments and other manipulative, interfering organisations (the EU, the UN, big NGO's (non governmental organisations).
If we don't reassert the influences that these two great institutions once held with out question, then our children will be looking at a bleak future, where individual freedom and liberty are long forgotten, or even dirty words.