I understand Ashley strategy and to be honest it does make sense with the amount of resources available to focus on something that can give multiplatform support without having to write different engines, and also have a very good editor to support game creation.
On the other side though I consider Html5 just another platform, like another console, that should not necessarily aspire to be compatible with everything.
Just like there are limitations right now to design a mobile game in C2 that the developers needs to take into account, the same could be said for a native engine and the multi platform incompatibilities. It is the developer job to know those limitations and either design for it or try to work around it. Don't have a 27.1 audio engine on ps4? Handle it with different assets or design your game against the minimum common denominator!
To bring an example to the table, Clickteam Fusion, does not have console support, but a few people actually made a fully native runtime for it. Yes, it does not support all of the objects and extension that Fusion has, but it works! And it lets people publish their game on consoles and other platforms.
http://mp2.dk/chowdren/