Not much substance I agree, but I do actually have sympathy for his argument. It's all well and good saying it's a matter of principle that a head of state should be democratically elected and not inherited, but the thing is we've got a system that kind of works. And it's not just us: Belgium, Denmark, Japan, Norway, Canada, New Zealand and Bhutan are all leading countries in terms of quality of life and low corruption, and they all have a constitutional monarchy.
This system we've sort of clumsily ended up with does give us a good balance. Our monarch has no bias towards any particular party and shows no sign of ever having any, and furthermore she's not motivated by personal gain. In a republic, the head of state will have a fixed term and therefore will have incentives towards partisanship and quite possibly corruption in order to ensure re-election. Key examples: USA, Iran, Russia.
The Queen's "powers" aren't really powers, and I think it's what she doesn't do that is far more important than what she does do. She must not ever abandon the democratic process because she will be immediately overthrown if she does. At the same time Parliament must continue to respect the democratic process lest they be dissolved at the Queen's order (probably a matter which would eventually be settled by the military, depending on whom they side with). A partisan head of state, in collaboration with Parliament could conceivably (whether likely or not) abandon democratic process, put their friends in charge of the military and corrupt the country. We have a system of checks and balances which could be weakened in a republic.
