I wouldn’t say that water-injected headers are safer, just less likely to burn the chrome off. You are correct about the Bassett valve not shutting off the water right away. Pressure will remain in the lines, injecting water into the headers until the pressure equalizes. I think it is best to have redundant safeties in place. Install a ball valve between the pump and the Bassett valve where it can easily be controlled from the driver seat.
Driver technique also plays a role. You don’t really want to just cut the throttle in a jet boat. The more that you load your pump, the more hairball the shutdown becomes. Instead, kill the water to the headers and then roll out of the throttle.
It is also a good idea to install a mechanical fuel injection pill (jet) in the water to the headers so that you can fine-tune the amount of water being injected. The fittings installed into the primary tubes should have no larger than a .028” opening.
Good luck,
Joe