As a Mac/iPad/iPhone user, these unusable sites annoy me too... but... Flash sites have been annoying me for years before the 'i' revolution. They have been overly complicated and awkward to use for a long time - so the quicker the millions of iOS users sound their death toll, the better. (Even adobe with various converter software etc have all but given in - cue the people arguing with me.
)
As to the heat & battery issue, universal, its just that really, the sheer amount of mobile web browsing is so much higher now than its ever been - the issues Flash caused were much less significant when we were all at laptops etc.
But anyway.... my real point...
Assuming you want to use the site for stuff not on the DLP App of course - get yourself a
Flash streaming browser! (Basically, the websites are processed elsewhere, and the result Fed to your phone. They are not as quick and easy, or 100% guaranteed to work on all sites, but have got me through the occasional Must-Use Site)
I use iswifter on the iPad, but I think that's not currently available for the phone (I suspect you could force it on there, but I haven't tried).
Try the Puffin web browser for your iphone, which as I type this is currently loading up the Disneyland Paris site just fine (including a pop up to ask if I want to play the embedded flash movie fullscreen.)
It isn't fast... but then, my work wifi at lunchtime is crippling slow!
** I will disclaimer this by pointing out that flash sites are frequently Not ideal for a touchscreen interface - and how well they will or will not work is going to vary wildly - and I've not tested the Disney site. I've played facebook games (the usually must-have requirement) very well on iSwifter though. **