CosmosDB does have problems but the comments here seem to mostly be about not understanding the data model. It's a JSON-based document-store that distributes data across partitions. It offers several interfaces (set at the database level) but that doesn't mean all the functionality is supported. It works well with MongoDB, Cassandra, and Table storage but you won't get relational SQL joins or fast graph search querie…
The problem is that their marketing and docs make it sounds like it is the solution for everything. Legacy Cassandra workload? Use CosmosDB Graph Database? Use CosmosDB Legacy MongoDB database? Use CosmosDB SQL Server database? Use CosmosDB When the only really valid use case is: Document Database? Use CosmosDB
Multi-model is a hard problem and only really works with similar data models. It's also confusing since people conflate SQL and relational semantics when it's really just a query language.
It does work well enough if you have an OLTP document use-case like MongoDB, Cassandra, and JSON/SQL.