According to the Cambridge Grammar of the English Language (CGEL), "attributive AdjPs [adjective phrases]" do not permit "prehead NP [noun phrase] modifiers". (See chapter 6, § 3.3, pages 551–2.)
Attributive refers to the common use of adjective phrases inside a noun phrase, preceding the noun that they modify. For example, in "a very short book", very short is an attributive adjective phrase. (Attributive is mostly as opposed to predicative — for example, "the book is very short" contains a predicative adjective phrase — though there also exist some less-common functions that are neither attributive nor predicative, such as in "as short a book as that" and "I want to read something short".)
A "prehead noun phrase modifier" is a noun phrase that precedes and modifies (in this case) an adjective. So in "a great deal wider", a great deal is a prehead noun phrase modifier (modifying wider).
So the problem in your example is that since "a great deal wider" contains a prehead noun phrase modifier, it can't be used in attributive position; *"a great deal wider accessibility" is not grammatical.
(In addition to an example with "a great deal better", CGEL also gives an example with "three years old": we can say "a three-year-old child", and "the child is three years old", but not *"a three years old child". It also gives a counterexample with "(a) lot": "She's a lot better player than me", meaning "She's a player who's a lot better than me." Though personally I find this counterexample pretty questionable; I would never say it that way, anyway.)
I don't know if that really answers your question "why", but at least it should help you understand the rule so you can apply it in the future. I hope that's almost as satisfying. :-)
