Shower head with easy on/off switch
There are certainly shower heads with their own flow control valves, and I know such valves used to be available separately to be installed between wall and head.

There are also mixing valves which separate temperature and flow, though most of the ones sold in the US seem to put on/off on the temp control, perhaps for some obscure liability reason.

So yes, it probably exists... But it may be hard to find or require importing.