Who becomes head of state in a republic is up to you. There's no reason it has to be an ex-politician – the experience of other European republics shows that voters often choose colourful characters who have achieved great things.
We could have an eminent scientist, a much loved writer, a respected sportsperson or someone who's made a great contribution to their community. It could be you or your children. And yes, it may well be someone with a background in politics, but they would be chosen by and answerable to the British people.
Democracy's unpredictable. Sometimes the result isn't what we would have hoped for and sometimes we regret having cast our ballot the way we did. But right now we have no choice at all; we simply get what we're given.