I am truly looking forward for CockroachDB to become the next PostgreSQL for planet-spanning database workloads. In our ecosystem we get more and more requests for CRDB integration.
Generally though, I would not say that full compatibility should even be desired. A k/v database simply works differently from a strictly relational database. There are things like shard IDs, avoiding hot spots, deciding on how to paginate data.
Going too much into "PostgreSQL" replacement will eventually hurt CRDB because too much focus will go into making legacy enterprise SQL (along the lines of https://news.ycombinator.com/item?id=25454635) work on this system. It's the forklift approach of moving to the cloud. This becomes clear when skimming through the docs:
I think many of the "light SQL" patterns are really great - things like SELECT or WHERE, which e.g. DynamoDB can simply not solve without ElasticSearch. But all in all, I am very excited for CRDB to get more industry acceptance, and I think their cloud offering could also become very interesting - a competitor to Google BigTable / CloudSpanner, AWS DynamoDB or Cloud SQL.