I believe the reason is that the term itself is used principally used to disparage modern rifles (and by association their owners) and to ban their use and possession.
I see no advantage in having a useful and workable definition for rifles of modern design using center fire ammo under 6.5 mm diameter.
I think accepting your definition means that an AWB would not affect AR pattern rifle in 7.62 or .338. For this reason I don't think the pro-regulation folk will accept it. Language has a purpose. Often the meaning of a term changes with time and is influenced by connotative use. For example, the term "dope" has come to mean "a drug taken illegally for recreational purposes, especially marijuana or heroin." When the drug "control" laws were passed, this term was used to broad-brush all the "drugs" except tobacco and alcohol. We're changing that now after dozens of years and an uncountable number of lives destroyed and money spent imprisoning those that used pot, not to mention the money earned by actual criminals in dealing and smuggling drugs.
IMNSHO many pro-regulation folk want to make a statement that the tools used by some mass shooters are indicative of mental or emotional compromise on the part of any owner. I have no interest in legitimizing a useless term to which they cling. Much like "nose bagger" was a disparaging term, I believe assault weapon is being pushed as a negative description. I haven't seen any positive uses for it. While many negative terms exist already (like war criminal) I am unconvinced we need this new one. YMMV 
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