I've thought about this question many times. I think that everyone would experience self destructive feelings/ thoughts when they need to escape. Everyone has their breaking point right? By self destructive behaviour I mean things such as binge drinking/ drug use that sort of thing. However if the behaviour is purely as a means of escaping rather than causing physical harm to their bodies then that behaviour probably wouldn't be classed as self harm in my opinion. For example my friend might think something like "I'm going to get drunk tonight just to forget the crap day I've just had" but wouldn't want the physical damage it could cause but if I wanted to use binge drinking as a form of self harm I would want that physical damage. It's a fine line between the two but if you're not intending to cause physical damage then in my opinion it's not self harm and so I wouldn't say that everyone experiences self harm thoughts. (Sorry if I'm not explaining this very well).
As for the more obvious forms of self harm such as cutting/ b**ning etc it's a little more difficult to truly know the answer to this. Where things like binge drinking are considered fairly "normal" behaviors and so get talked about more, things like deliberately cutting yourself aren't talked about much. I would say that anyone who thinks about self harm would have to be very distressed and not everyone experiences that level of distress and so are unlikely to think about harming themselves.
I could be completely wrong of course. My definition of self harm thoughts/ behaviour could very different from the opinions of others...