If anything, it'd be the other way around. It's been argued that mass extinctions actually promote evolution rather than inhibiting it. Not only do they create new survival challenges that life has to adapt to, but they open up environmental niches for species to evolve into, so they create new opportunities for evolution to happen. And reducing a species' population to a small number increases the probability that a new mutation can survive and spread, because it'll be up against less competition, so statistically speaking, it's less likely to be crowded out of the gene pool. Indeed, the evolution of hominids
seems to have been jumpstarted by a partial mass extinction caused by a nearby supernova a couple of million years ago.
So a planet in a quieter part of the galaxy, one that was subjected to less frequent mass extinctions, would have less pressure on its biosphere to evolve and adapt, and would probably have much slower evolution. After all, evolution isn't some inevitable forward progression built into our genes, like fiction tends to misrepresent it as. It's a process by which organisms adapt to environmental change. Thus, the rate of evolution is linked to the rate of environmental change. The more the environment changes, the more life evolves. Sure, there's probably a point at which the stress of constant global extinctions becomes too much for life to rebound from, but in general, a more turbulent planetary environment would promote faster evolution.
And of course evolution isn't some inevitably "upward" progression like your examples suggest. There's no direction to it, beyond the selection for a greater ability to survive in a given environment long enough to reproduce. True, there is a theory that thermodynamic forces tend to promote the rise of intelligence because it allows the creation of more future possibilities and thereby increases causal entropy, and that there's a "
cognitive niche" in evolution because intelligence and tool use create new possibilities for adaptation beyond what genetic evolution is capable of by itself. But evolution isn't a ladder. Intelligent life forms are just one branch (or a few branches) on a huge, ever-growing tree, the vast majority of whose branches are microorganisms and plants and insects. Intelligence is one survival adaptation out of many, not an ultimate end goal of the evolutionary process.