SA, I'm glad you posted the link to the Monkees singing "Riu, Riu Chiu."   It shows very well how good they were musically, at least after they got out from under the thumb of the managers, etc., who tried to keep them in the box of teenage TV pop.

In the later years of their career, when they were allowed to play their instruments on their records, they showed that they really were pretty decent musicians.   I don't know the extent to which they grew into that as their teen idol careers progressed and the extent to which they were just allowed to display what they already had, but even Jerry Garcia acknowledged that "their records are pretty good."