At the end of the day Construct 2 is an HTML 5 game development environment. That is what it does. If HTML 5 does not meet the requirements of your game, then there is really nothing Construct 2 can do about that. Any export options are going to be wrappers that wrap an HTML5/JavaScript game. It does not make native apps, it wraps HTML 5 in a native app wrapper, but it is still HTML 5 underneath. Some wrappers may accelerate it more, but at that point you are looking at the developers of those wrappers.
Construct is run by a 2 man team. Most of the teams working on these third party wrappers are bigger than that. The developers of those wrappers also tend to make plugins for Construct 2 and other engines as well. Construct has a published SDK that can be used to create plugins. It benefits the wrapper developers more to develop plugins to work with each of the game creation frameworks than it does for the game creation tool developers to try and figure out how all the wrappers work and then try to integrate them all into their tools. It is also much more efficient as focusing on making sure all the platform and wrappers can be directly integrated would take up the majority of their time and no new features or optimizations would happen to the core product. What makes more sense, having the folks who write the wrappers and know how they work make the plugins, or having the folks who don't work on the wrappers every day work on integrating them?
At the end of the day the question is does HTML 5 support everything you need currently for your game to work the way you want it to? If not, Construct 2 can't change that for you. Not trying to sound critical here, but your expressed concerns are based on the current reality of HTML 5 game development. Internet standards is a term very loosely used by the browser and platform vendors, and vary wildly from one to the next. Third party wrappers like CocoonJS, AppMobi, PhoneGap, et... are looking to level the playing field, but the are still early and constantly being improved. You may also notice in these forums that many of the teams that develop these wrappers also support construct 2 and are actively working on plugins for it. The wrappers weren't created because of a lack of features in Construct 2, they are created because of a lack of uniformity and standards across the HTML5 landscape in general.
Any how, sorry for the long winded rant, I haven't had my coffee yet...