Why would you rewrite all your apps with something other than PHP? You wouldn't, of course.
Why would you consider a language that wasn't "designed specifically for web scripting"? Because that's an irrelevant criteria for choosing a platform. It makes no difference if something was(n't) designed for a single purpose, only that it is effective for the purpose you require.
A third language worth considering -- how about JavaScript w/ Node.JS?
Benefits to writing web apps in a language other than PHP? Well, you get the benefits of that language - whatever those might be. Benefits might include anything from technical superiority (and what 'technical superiority' means is based a lot more on the application than the fact it's web-based) to it being easy to find developers who know a platform in your city when you need to hire, availability of documentation, or even the general progressiveness of the whole ecosystem (is new stuff happening? is there community interest?).
I think that discounting everything but PHP just because they aren't pigeonholed into web apps (of course, PHP can be used for more than just the web, but let's gloss over this fact) is pretty... close minded.
A counter question: if you like PHP and are productive/happy/etc using it, why would you go out looking for new languages to replace it? You will only discover that they aren't PHP.