Cisco 9000 Series is well suited anywhere that requires lots of room for FIB (e.g. holding multiple full tables in multiple VRFs for militancy). It is also well suited for carriers due to the feature set - they can do MPLS and they can do segment routing. They are less suited for shops that have always been Cisco shops that are looking to replace their IOS devices in the least-difficult way and without having to learn new CLI. "IOS" may be in the name, but it is not at all the same.
It is well suited as a large router in a data center handling extreme amounts of traffic. It offers room for expansion and upgrades. It does not work well as a customer premise device due to its size, power, requirements, and cost. There are other ASR models better suited for such cases.
They are fitting nice in a multi-tenant environment where we need to separate customer loads in a secure way. In our environment, we use Cisco routes in multiple locations for many purposes and have not found a non-suitable use case yet.
In some small installations, we are also using some other routers, like in a lab or test environment.
Any large enterprise with large throughput requirements for their business-critical infrastructure should use the ASR series routers without exception. The licensing cost might hit your pocket hard, but with the exceptional performance and reliability that the ASR series offers, it is easily the best option available in the market. It is the "tried and tested" router. Don't think twice, just go for it!