It is possible to perform effective UAT with very lightweight cases, but this depends on the system knowledge level in the users performing tests. If you don’t require extensive detail, there is no reason to put it in the test case.
Historically, detailed test cases and scripts also helped define what the tester was doing so any issues could be described in the context of that series of events. Modern UAT, however, uses capturing technology showing precisely what the user was doing and documenting their concerns and feedback.
Regardless of the approach, your UAT will take, test cases have become valuable assets that we want to re-use, and hence they need to be stored and organised in a way that supports that.