The simple existence of level or contoured tones in a language is not a problem for the SPE theory of representations, which is why when the focus was on just reducing tone contrasts to some minimal system of pluses and minuses, it was always possible to come up with an arrangement. You find rising and falling tones along with level tones in various "dialects" of Chinese, Vietnamese, Zapotec, Mande, Kru. A really simple reason why a large number of tones doesn't matter is that you can enumerate them Chinese-style ("Tone 1, Tone 2..."), and any number can be trivially translated into a system of plus and minus values, for example an 8-tone language requires only 3 features.
The problem of contours really stems from the need to group together subsets of tones into "natural classes", because in rule systems, particular subsets of tones often act together. So just as [p t tʃ k] often act together in a way that [p t tʃ l] do not, you find recurrent groupings in tonology. The interesting thing is that the possible groupings looks completely unconstrained if you just look at the tone-pairings, but if you look at the pairings plus their order relative to the trigger sets (and the composition of the set), tone groupings become very limited. An example is that H becomes F before L and R: but, H becomes R after L and F. L becomes R before H and H, but L becomes F after H and R. The various other "level becomes contour" possibilities that you predict from randomly grouping together two of the tones {H L R F} either before or after the target tone simply don't exist.
The explanation for this is straightforward if you decompose R into "L+H" and F into "H+L", so these processes reduce to H → H+L / _ {L,L+H}; H → L+H / {L,H+L} _; L → L+H / _ {H,H+L}; and L → H+L / {H,L+H} __. Which generalizes to "attach the preceding/following tone to this tone".
