The word “able” is certainly a free morpheme. The relevant question is whether “able” and “-able” represent the same morpheme. The identical spellings are actually somewhat of a coincidence, as they have different etymologies. The “-ble” parts have the same origin, but the A's don't: the word able is from Latin hăbĭl-, which came from the verb hăbeo + the suffix -bĭl- (one of the B's was apparently lost by haplology), while the suffix -able is from Latin -ābĭl-, which came from the suffix -bĭl- combined with the A-vowel that occurred at the end of "first-conjugation" verb stems.
But I don’t think etymology by itself is a full explanation for why “-able” would be analyzed as a different morpheme from “able”.
I think it’s relevant that the distribution of “-able” looks like the distribution of a bound morpheme/affix: there are words where it triggers a (sometimes optional) stress shift, such as “preferable”, and there are words where it combines with a bound morpheme, or at least a specialized allomorph that cannot occur freely, such as “despic-“ in “despicable”.