Zarathustra said:
Just curious, is that de facto symbolic? Has there been a recent instance where the queen has vetoed something passed by parliament?
I would imagine if the royal family actually tried to leverage that power their gig would be up pretty quick.
Yes, if the sovereign decided to override the will of parliament, that would probably be the end of the monarchy. However, there are theoretical situations where the sovereign might have some discretion and might actually get to make a real decision. The first is if you have an election that produced a true stalemate in parliament. There are "rules" (really, just conventions) as to who the sovereign should call on to form a government, but if the UK ever had a really splintered election result, it's possible to conceive of a scenario where the sovereign's decision as to which MP to call upon to form a government might be crucial.
The other area where it comes up is when you've got things going on outside the realm of established practice and history. We saw this during the post-Brexit election maneuvering, largely as a result of the fixed term parliament act. Prior to the passage of that act, whenever the PM lacked a majority to get legislation through parliament, one important option was the ability to call for a new election to seek a mandate from the voters. However, the fixed term parliament act (passed in 2010 when the Conservatives entered into a coalition with the Liberal Democrats) removed that discretion from the PM, and required a super majority to call an election early. This left the government in limbo when it couldn't get Brexit bills passed, but also couldn't go to the voters to get a mandate. There were some possible moves that might have involved the sovereign exercising some discretion if the Remainers hadn't finally taken the bait and voted to hold an election (resulting in a huge victory for Johnson).
If you don't have a monarch, in a parliamentary system, you have to select someone to be head of state to fill the same roll, and being a politician, this person would be much more likely to get involved than a monarch would be.