A question about sentence typology

Is the categorization of sentences into simple, compound, and complex established firmly by the rules of the English grammar or is this compartmentalization merely a simplistic way of looking at the English sentence?

Take for instance, the sentence You must be joking about the ongoing crisis in their family.

The part You must be joking can well stand on its own as a complete sentence and the presence or absence of the PP doesn’t really change the type of sentence it is.

Similarly, First deserve, then desire lends itself to a similar treatment: (You should) first deserve can stand on its own as a complete sentence. I suppose it is again a simple sentence like the former. But one might as well argue that the clause (You should) first deserve, is (logically) dependent on the second clause that follows the comma, which makes the sentence complex.

As indicated earlier, my question is about the merit of the sentence typology and its scope.