Only issues I've ever encountered/worked on with FZS1000's coolant system, other than union or hose failures is:-
Fan thermo switch failure, causing overheating in heavy traffic/hot weather. This was mostly down to corroded connectors.
Fan failure due to over zealous jet washing.
Thermostat failure, very rare.
Blocked carb heating circuit, restricted rads and failed water pumps. Are all in my experience a direct result of owners/stealers not using the correct coolant or when the system starts leaking due to union/hose failure they top up with just tap water or using no coolant just tap water. The other is when the engine is worked on and the system not only is filled to tap water mix, it's filled incorrectly causing air locks.
Tap water will and does rapidly cause corrosion even if the coolant is at the correct ratio, this rapidly turns into slit which buggers water pump bearings, blocks the cab water heater system and rad cores. I've also seen cheap pattern parts fitted due the above mentioned fail in short order.
Basically there should be NO rust staining or coloured coolant, if there is the cooling system has had tap water added and the steel elements (water pump, elbows, unions and ridgited pipes) are corroding.
A well maintained engine/cooling system should use almost no coolant, if it is something is wrong. Only ever top up (expansion tank) with either pre mix or concentrate coolant NEVER use tap water only demineralised or deionised water. Only change the coolant if it fails a hydro test, the coolant on my FZS600 is the same that it was supplied with, I kid you not.
As stated earlier and in my experience I've never known a jap bike water cooling system to fail (over heat) due to a design flaw, they if anything over cool. Requiring replacement thermostats to be fitted during recall or standard servicing, others GPz900R spring to mind had water temp senders replaced as they were rated to low and the temp gauge would go into the red at the hint of any traffic. They went from black to pink or the other way around can't remember now.