Certainly, putting this URL on a page for other people to read is a very bad idea -- like tossing your (physical) wallet out your car window.
The intent of the URL is that you should bookmark it and otherwise keep it private.
Unless you know of some way for an attacker to get at the browser's bookmark list (which I'd be interested to know about; I'm certainly not enough of an expert to be sure that no such attack exists) then this seems fairly secure.
The tossing your physical wallet out the window analogies are tired and false. When does your wallet ever have thousands of dollars in it? Some naive BC users had huge % of their net worth in BC then got punished for it in various ways.
I have tried the service and I also understand bitcoin to a certain extent. That is why I recognize that "address" in this context is not a URL but a bitcoin wallet ID or address.
Did you know Google will still index URLs prohibited by robots.txt if it finds a link to them (it just won't crawl them)?