There is no clear '4 years to election' as they have in the US.
In my home country, Canada, it gets dicey as we wonder sometimes just what the 'Governor General' (Queen's rep in Canada) will do.
I don't think the Queen is going to be interjecting on any 'legislation' unless there is something fundamentally unconstitutional about how it was passed; but there's definitely some question marks about 'how and when government falls and is formed' - and especially, how 'minority governments' are formed. If there's no obvious winner, then minority situations form, and it can get weird.
That's still a thing.
I suggest the US would have been a better country were the American revolution to not have happened. Sounds totally crazy, but true. I think the US would have healthcare, be a bit more socially minded, slavery would have ended a lot sooner, and the US still have all of the 'good parts' (except a cool national anthem).
There has been a lot of speculation over the years about whether Charles might be a more activist monarch, but I’ll be really surprised if he actually tries to exercise any of his theoretical powers. He might be a bit more outspoken in public, and do a lot more lobbying in private, at most.
Otherwise, we might need a 'Supreme Parliamentary Council' to basically enact those duties, and if any members of Parliament didn't agree on the outcome, they'd take it to the Supreme Court who would rule on it kind of thing. Something that would only happen 'once in a century'.
Where there are Presidents, it's generally straight forward: the Dude with the most votes (of whatever type) is the Dude and that's it. There can be voting shenanigans but generally not outcome shenanigans.
I'm fine the way it is in the UK and Canada, I wouldn't change a thing.
If we want reforms, we can do that at more operational levels, aka 'governance by blockchain' to put it in 2019 Valley terms.