What are the demerits in a Shakespearean sonnet ryme scheme like couplet and quatrains?
A fascinating question. The demerits or weaknesses/flaws are corollaries of the rhyme scheme's strengths. By that I mean, the couplet provides easily understood order and regularity. It provides structure. It allows a kind of predictability. Combine that with the rhythm and you have a poem that in its structure indicates a known and knowable world; there is a large degree of safety to the structure, and in a way it is game like. It is easy to evaluate as good or bad.
By contrast, the weaknesses to such a structure are that it can force order on disorderly subjects. It creates order and structure and at times that is false. It may overly simplify and lighten its subject matter, and the structure makes philosophical claims for a knowable universe that are, in some cases, too extreme.