Okay, so as to not straw-man your point, I won't list the cons to having the Queen as-is.
But here are the pros.
Revenue: Neverminding crown-lands, which if you went republic and seized all royal lands you would control all the revenue from, the tourism connected to the royal family is 1.7 BILLION pounds. Annually. You would be getting rid of that by getting rid of the queen, and no, without an actual royal living in the castles, they wouldn't nearly bring in so many tourists. You never hear much about Frances castles being tourist havens, do you?
Yes, it is only 0.2 percent of your imports, but still. A pretty penny all it's own.
International regard: People think the queen is nice. Basically it, but reputation is good. A friendly face does wonders. Might go away once you get a King, but still, just talking 'bout Lizzy here.
Internal Politics: Power. Having a focus for personality allows gives people a good outlet for patriotism, so it doesn't get bound up in someone who actually -has- power, and can do terrible things with that power, safe with the support of the people. Cult of personality, yeah. Also leaves the people with power relatively safe from tabloids. The tabloids focus on the royal family, and the ministers can do things without worrying for their reputation as much as they otherwise likely would, since it's less likely to be considered "juicy" enough to get published. Worrying about their reputation would lead them to do things that look good, but don't actually -do- anything. I'm sure it's a problem there, but it's much worse in the U.S. and to a lesser extent, Canada. (We still have the queen, but she's not like, central or anything. Prime Minister acts more like a head of state than as a head of government here)
The queen serves as a lightning rod, basically. She sucks up all the patriotism, leaving it safe (patriotism is radioactive, man), brings in more money than the royal family sucks up, and relieves a lot of ire the Brits might otherwise face internationally.
Those are your pros. What are your cons?