It has a MongoDB API Layer and a Cassandra API Layer (as well as SQL which is preferred).
Works just fine, apparently cost can blow out though with high usage, I haven't got there yet.
Does have a free tier.
The former, lift and shift scenario I can understand as you need to structure your data to work best with CosmosDB/DynamoDB etc. If it's the latter that is useful to know as I'm currently building a POC on Azure so I should watch out for it.
This was all part of a benchmarking exercise to figure out how to scale an app with minimal changes so we expected some performance penalty, just not as steep as what we observed.
However, CosmosDB is a managed service, easier than setting up your own database. Did you exclude Atlas from your conclusion for some reason? Ie did AKS do things that Atlas could not?
You must be diligent to develop your application to use it efficiently from both a cost and performance/latency perspective.
Those that put in the work may not love it, but they are very successful at operating at scale. Massive, insane scale.