You misunderstand what Gould says. PE doesn't say that
all evolution is fast. And there is evidence for slow change so it would be wrong if he did.
What PE says (and the math of genetics does too) is that speciation events will often happen with a small founder population. That in this smaller population evolution can move along faster than the broad average. Since the population is small it is not likely to be well preserved.
If nothing allows for the separation off of populations and if there are no new selective pressures large populations will remain comparitively static. But
notstatic.
None of that suggests 'spontaneous'. It does suggest damm fast, like 1,000's of generations.