We've been converting all of our tech to feed off of our hypermedia datasources over the last 3 years. At first, the big bang was simply the data connection. I had a hard time seeing big value in the hypermedia part. That is, until we needed to build our mobile solutions.
Before I go to far I'll say that we are using ionic, so purist will scoff (kinda silly really). Works for me, we are completly cross platform with a single code base, develop at warp speed, and my customers don't see a difference. Additionally, we have the most robust line-of-business apps in the marketplace (ServiceMonster) and we are still 3 weeks from release.
The hypermedia's big bang come from two things: our mobile developer was new to our team but was able to blast through the API with no docs and proper end point hookups, even though he never heard of REST or hypermedia. Second, because my data agnostic content type (Morpheus), we get TONS of client goodies such as auto validation and standardize collection handeling.
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