Construct will never do "native". It just doesn't work that way. But I think the underlying architecture (html5) in C3 is not an issue in this respect.
While this used to be a real disadvantage to Construct a couple of years ago because of horrible performance of mobile games created in it, nowadays there are more and more devices that can handle it perfectly well. So... if you want to focus on mobile, just focus on mobile -- C3 is well equipped to do that.
That said, I'm a bit concerned about the sustainability of HTML5 in general. After all, it is not a programming language, it's a front-end website language. So what if the same thing happens to it that happened to Flash? What if HTML5 changes in some way that's incompatible with using it for making games? What if HTML6 breaks some key features in terms of backwards compatibility? What if, for whatever reason, internet browsers change how they work and it becomes impossible to wrap them in mobile apps ? blah blah... Le'ts hope Scirra will just follow along those changes.
PS. Frankly, I'm surprised "pc browser games" are still a thing at all. Does anyone earn any kind on money on those?