In regard to the Imperius, it's possible that an imp's natural "cloaking" prevents potential masters from being able to remember them long enough to make practical use of them. It's also possible that they don't speak human languages. Has it ever been established how Imperius commands are conveyed to targets?

Maybe even a captive imp is too well concealed to Imperius, although if they're that well cloaked it raises the question of how people even know they exist.

In the original canon, Crouch Jr. as Moody was able to Imperius a spider, which implies that it does not require that the recipient have human language capacity, or even be intelligent.