"autodidactic" is "autodidact" + "-ic" rather than "auto-" + "didactic"; this is not a pedantic distinction because "autodidact" has mostly positive connotations, whereas "didactic", as you note, often has connotations of unwanted moralising.
the same features make it a wonderfully fun language though :) my favourite example of how building up a word differently changes its meaning is inflammable (inflame + -able, rather than in- + flammable)