Is there any overarching reason why, after excluding the infinite classes of finite simple groups (cyclic, alternating, Lie-type), what remains---the sporadic, exceptional finite simple groups, is in fact a finite list (just 26)? In some sense, the prime numbers can be viewed as "sporadic," but there is an infinite supply. Is there some principle that indicates that there must be only a finite number of these exceptional groups, and the "only issue" (to minimize a huge, multi-year community effort) was to identify them?
I ask in relative ignorance of modern group theory, and apologize in advance for the naiveness of my question.