For me there's no denying that a Monarchy is a bit of a silly institution in this day and age, but it would be wrong to suggest that it doesn't serve any function. I certainly can't see how making a career politician Head of State is going to improve matters. President Cameron anyone? I was actually talking to someone the other day who met the Queen when she came to Manchester recently, which was a source of enormous pride to them, which you wouldn't get to the same extent if they'd met a politician, so there is a bit of 'stardust' there too, although there is a 'distracting the masses' counter-argument to that too.
The tourism argument is a bit simplistic imo. I'm not entirely convinced that Yanks come over here because the Monarchy is still in situ, but it remains the case that Western European economies are going to be faced with a whole range of threats and opportunities in the decades ahead from emerging nations such as Brazil and India and Britain's image as a quirky nation with some eccentric long-standing traditions will be our best way of selling our products such as Malt Whisky and Bentley cars to those nations. The monarchy is part that. If we play things right as a nation we could be far better placed than other Western nations to be perceived as a hallmark for aspirational consumer goods when the aforementioned countries start to provide a free spending middle-class running into the hundreds of millions. On that basis the monarchy would easily pay for itself and the tourist argument is rendered largely irrelevant imo.
As to the actual question posed in the OP, I've said it before on here, I believe she is a remarkable and formidable woman. I look at what she does and would say that it's significantly above and beyond the call of duty. Most of it must be incredibly boring. Whatever people think of her in this country, she is held in incredibly high regard throughout the world and is a very adept diplomat. The skill with which she dealt with her Irish visit and the positive vibes it generated were a master class. She has also always had the measure of her Prime Ministers too, Harold Wilson being her favourite iirc. When you think of the changes that she's witnessed throughout her reign it's pretty incredible that she's still considered to be appropriate to be Head of State by the vast majority of Britons, and a testament to her survival antenna, notwithstanding the Diana situation.
The economic argument apart, I would be ambivalent about the Monarchy withering on the vine after she dies. I can certainly see some merit in that happening because one of the pitfalls about such a system is you can't, as a people, pick and choose your Head of State, or get rid of them if they're poor at the job. However, I believe in this woman we've been lucky to have someone with the brains, people skills, work ethic and sense of duty to serve our country extremely well.