My old trailer had a black tank flush, I used it to clean the tanks at home between trips. Never had a smell while camping. Then the hose broke, and I capped it off. Went another few years with no tank flusher. Still never had a smell lol.
I do notice some pretty bad smells when actually dumping, and sometimes the grey is as bad or worse than the black. but I think it's just the smell of the water in the tank, not something a rinser will really help with.
I could see the benefit for someone who keeps the drain open, it does seem more plausible that 'stuff' would remain in the tank if always draining. Though even then it seems like a good shower would rinse it out.