You did, however, forget the rather unfortunate fact of DRM. Content Providers will always want their content protected, and will charge a lot more if it is not, even assuming they allow the content on iPlayer unprotected in the first place.
Also, as you say, there is the problem of availability on multiple devices. Flash, for all it's faults, does embody the idea of "Write once, run anywhere" well.
The problem that HTML 5 has at the moment, which, I believe will stop it becoming a defacto streaming standard is that content providers will want to use one codec that they know will play on everyone's browser. They don't want the hassle and expense involved in supporting multiple codecs. For HTML 5 to be widely used by the Media companies, it needs two things to occur.
1) It needs working DRM, and
2) It needs all the browser manufacturers to agree to offer the same codec, or both codecs.
Sadly, No 2 is not likely to happen. Microsoft and Apple get royalties from H264, so they are unlikely to want to give it up. Mozilla and Opera need to keep browser costs down, so it's in their interest not to pay royalties if they don't have to.
Oh, and for the record, I do not like DRM. Being a Mac and iPhone user, I consider Flash a necessary evil rather than something good and despite it now being owned by Google, I'd like to see webm succeed.