Her role seems to be that of a rather pointless rubber stamper.
Well, she's the Head of State. For a couple of states, actually.
In the US, the Head of State is the same person as the Head of Government, and there's quite a bit of thought that it causes us no end of problems, because it means that you can't be politically opposed to the administration of the Head of Government without, essentially, being in opposition to the embodied State. People often wonder why American politics is so much more tenacious than in other countries, and I think that's part of the reason.
Not having a King or Queen doesn't mean you get to avoid the boring ceremony - memorials, awards, etc. Having a Queen means that you have someone specifically dedicated to the task. In our system of government, Barack Obama has to take time out of running the country in order to pin medals on soldiers. I think we'd be better of with some old bint to handle all that stuff.