Short answer: it's not the "istic", it's the underlying "ist", or ultimately ism.
Let's examine your four examples:
negativistic: "negativist" + ic: being like someone who
has a tendency to be unconstructively critical
simplistic: "simplist" + ic: being like someone who
"studies simples", which are "herbs used in healing, medicine of one ingredient only; the notion being that each herb possesses a particular virtue, thus a `simple' remedy", thus a simplist is a person who subscribes to a theory which is over-simple, trying to explain too much by a single principle
moralistic: "moralist" + ic: being like someone who is
given to moralizing, which (in the perjorative) is "indulgence in moral pronouncements; the exposition (often superficially) of a particular moral code"
legalistic: "legalist" + ic: being like someone who is
like a goddamn lawyer
So each of these words, rather than directly ascribing a quality, is defining the trait in terms of acting like an a -ist. This is not obvious at first blush, because the -ist has been subsumed into the -istic, sometimes to the extent that modern English doesn't even have original -ist (or -ism) any longer, as in simplism and simplist. But none the less, in each case, the etymology traces back to a form of "X-ist" + "ic": "acting like or having the quality of an X-ist".
So to the extent -ist s and -ism s often have negative, pejorative connotations, so do -istic s. But while ists and isms as a class are charged with obdurate or doctrinaire (and often supercilious) qualities, whether particular ists and isms -- and by extension, istics -- do, depends on society's perception of that particular doctrine.
Consider the range of senses in altru-istic (positive: one who practices altru-ism), sad-istic (negative: one who follows de Sade), art-istic (neutral/descriptive or positive), unart-istic (neutral/descriptive or negative), character-istic (not even applicable, because it doesn't derive from an ism), bolshev-istic (positive in Soviet Russia, negative in McCarthyist America). The overtones come from (society's perception of) the root ism in each word.