Not if they're already made in HTML5, especially if you're supplying support for both flash and HTML5. The space bit, I have no idea.
A lot of flash games out there can't be handled by mobile devices anyways. I tried playing Axon on my Samsung Galaxy Player, which is pretty new, yet it crashed after a minute. It has 384 MB of RAM (more than the iTouch), while most of the leading smartphones on the market have up to 1GB of RAM, which even then might not be enough. (It depends on how many apps you're running. My player usually runs at about 200MB out of the 384 provided, with no active apps running.) Even modern tablets only have 1GB of RAM at most, and for tablets there would probably be even less memory to handle games.
All of that, not to mention most games would need a keyboard and/or mouse to play anything. It would be easier to just release the games to the app market, specifically designed to be played on mobile devices.
Also, did you know that most, if not all of HTML5 games run off of one line of HTML code, and the rest Javascript? The 'constantly improving' bit is sort of irrelevant. Any parts of HTML5 that are improved and added in the future wouldn't have anything to do with the games. There's also the trouble of getting all of the things needed for the game to AG (all the art and code), while for flash games, they are in neat little packages.
While it would be cool to have HTML5 games in addition to flash games (I might even be inspired to make a game, if I could figure out how), I'm not sure if most of the argument is there.