If we use Flash for anything, our marketing angle is affected: we regularly say we're 100% Flash-free, pure HTML5 only, and we can't say that if we depend on Flash anywhere.
On top of that StatCounter says IE7 has less than 2% market share worldwide and IE8 has around 15% and still falling. Sooner or later these browsers will be dead so we don't want to do a lot of work for browsers fast becoming obsolete.
You can install Mozilla Firefox, Google Chrome, and Google Chrome Frame without admin permissions now. So even if you're on a locked-down PC with limited permissions, you can still usually install Chrome Frame or another better browser and you're good to go.
If schools using IE8 or earlier want to install Construct 2, we tell them they need to upgrade before using C2 because those browsers are not supported. I think trying to get a modern HTML5 tool like Construct 2 to work with old browsers is kind of obtuse, these browsers just don't support HTML5 and hacks like this will be plagued with lots of little broken features like I mentioned. So we don't want to have the support headache there either. If they need IE for compatibility, they can install Chrome alongside IE and just set Construct 2 to use that. And as a nice bonus, now they have a better browser than IE :)
So there you go, it may be possible but it will probably be slow and buggy and difficult to support and maintain. So we won't support it - install Chrome instead!