There is a fantastic post by Ben McCormick about the up and downsides of this system: http://benmccormick.org/2016/09/19/testing-with-jest-snapsho...
Snapshots aren't the only feature of Jest; it is simply one assertion in our assertion library. There is a ton of other stuff in the framework that makes setting up a test environment and writing tests easier.
My philosophy for building a test framework is to build a good feature set to help you out in any situation but the user should be in total control. This allows you to find the best way to test your code which I've found to be extremely subjective. The choice of test framework and test methodology seems almost religious at times and I've deliberately tried to stay away from these conversations.