Yeah, I think it mostly makes sense when the required hardware to run your programs is really expensive and you have multiple user that need to access/control the system or you need to do it from multiple locations. Either giant data sets (corporate or government databases) or speed requirements beyond the reach of mass market desktop computers. For ordinary collaboration and remote work situations, cloud computing (that unfortunate name for keeping & sometimes sharing your files on a remote servers) works better.
This is classic usage of client-server solution, not thin client.
Client-server solution (compared to SW running on a single host, that's usually a PC) are used in the following situations.
1. The data should be shared by multiple hosts/people, making copies and modifying them on each host does not work. - The most classic use-case. The server manages DB (+plus some computation/manipulation on them if needed). Client relies on server for the management/manipulation of the data and focus on user interaction (presentation of data and UI).
2. The computation and/or data size exceeds the capacity of typical PC that it should be processed by a big iron or cluster of computers. Again backend server (can be cluster of computers) does the hard work and client is responsible for UI.
None of the use-case automatically makes the client thin.
Actually most clients are thinner and lighter than servers. "Thin Client" is something that is thinner than typical PC/client.
IIRC, Thin Client came to the world with the claims like below.
* By delegating computations to server, you can use cheaper HW instead of typical PC (of the time) as a thin client and save money. - At the time, primitive RDP/screen sharing and the dumb Web was used.
* (Not sure this was claimed at the time of birth, but anyway) The management/maintenance is easier because you don't have to migrate data when you have to replace the PC, nor you have to back up each PC. And as you don't install all kinds of apps to the PC it reduces the works of IT.
Anyway none of your claims are about Thin Client, they're about client-server model (which includes most of the cloud computing).