I would say the editor overhaul is much, much needed.
Also, not being native is not the only issue, some things in C2 are just not good enough (keep in mind that a game can have some crappy optimised parts and still run perfectly, a game engine not so much, as each quirk will be present in every single game and if someone is to rely on them well..):
-AFAIK, the collision system is not perfect, ok, they used collision cells to make it "useable in larger worlds" but this is still a potential issue and bottleneck (I know, is overllaping is faster, but it is still not as good as it could be)
-events runs on a single core, and other parts of the engine do, I know it might not be a big deal but I think some progress could be done regarding that (as I think big limitations can be implied with a multicore system)
-the physic engine is simply not as complete as it could have been as far as I could gather, also, it is totally framerate dependant by default, try on a 120Hz monitor and the simulation will be twice as fast, I understand the logic behind that though (this may be the only case where locking the framerate to a value is a valid choice)
-something doesn't work? Welp, too bad that thing could potentially break projects, won't fix
-Users would rather rely on using events directly rather than using the plugins, if we are to reinvent the wheel, might as well go with another engine
-third party plugins and official plugins are not treated equal, third party plugins are updated by hand, official plugins updates are tied with the engine (a quick analogy with IE updates being tied with windows updates in the past is enough to show how bad it is), also, needing to update third party plugins by hand rather than having basically a way to open C2, check a plugin store list, see which one can be updated and the changelog that goes with it (official ones too) would make using third party plugins a breeze I think (and believe me, some third party plugins are nice).
More related to the exporters now:
-well, this one is a big one : limitations are not consistent, they simply aren't, two differents hardware can work the opposite way we would expect them to, just by virtue of blacklisting, we can turn blacklisting off ? Hurray, but then the device simply does not support webgl and just displays a black screen, what then (my netbook will not support webgl, ok it is outdated but still, if your plan it to make simple games, it will even fail in that regard)? Or if the blacklist fails (AFAiK, I cannot turn webgl back on chrome on my galaxy tab 3, not that chrome was a good android browser experience anyway for me, but still that is a problem)
-kinda related to the first one, games are not future proof, they are not dependant on browser features only, if one browser decides than it is over for platform X, then it is over for it, end of the line (I know nw.js and the likes can be a partial solution to that, but let's be honest a second, why people wanting to make a browser game exclusively would want their users to download an executable, it is even worse than downloading a plugin).
We will always rely on third parties, yes
We will probably won't benefit from having native exporters due to the amount of time needed to polish it, probably
We can rely on browser vendors to keep things working in the long run C2 wise, absolutely not, They simply don't care enough for that, I would not be surprised to hear that chromium guys are only testing the most games related features on chromebooks, also mobile web browsers have issues that simply breaks games (the slow decoding chrome issue alone can render your game a painfull experience on mobile, we also had the time when a beta webaudio api was used in C2, and broken by chrome to the point it was unplayable), that doesn't mean we cannot do anything great inside a webbrowser (..well from an economic standpoint there is currently no point in doing that but I am staying in the non commercial kind of things) but we need to be sure they won't screw us with one change, or to be able to face it without issues.
As for unity, for a native experience it is good, but from a webbrowser one I would be curious to see if it is worth it (not with the web player plugin obviously)