Is it because aircraft can get more "instant" power for go-around, with throttle full-forward?
Or is it for protecting the aircraft's engine from high RPM, low PROP stress in case of go-around?
It's both, but mostly the first one. You need maximum HP for go-around, which means you need the propeller governor regulating RPM at redline when you call for max power.
You could leave the prop control at a cruise RPM setting, but you would have to remember to move the prop RPM to max before the throttle if you have to go around. Easier to save time and just move the RPM to max while on approach so it's ready when you need it. On a piston twin, where you need every fraction of a HP from the good engine if an engine quits on a go around, this can mean the difference between making it and not.
If you leave the prop at a low RPM setting and forget about it when you need to go around, and just shove the throttle forward, you will be at max manifold pressure but with RPM limited to the governor setting, and you won't be getting maximum HP for the engine, and there is a possibility of inducing detonation from the extreme "oversquare" operation, oversquare being RPM lower than MP, especially on a supercharged or turbocharged engine (you won't ruin a Contintental O-470 doing that, but shove the throttle on a supercharged R-985 to get redline MP of 36" while leaving the RPM down at, say, 1200, and you'll probably blow a jug or two).
Having your props taking smaller bites of air means that you get faster response from increased throttle, allowing you to reconfigure from landing to missed with less flailing about. There's an additional benefit at lower throttle settings: you get more drag since your prop is the literal opposite of feathered, so if the air it hitting the prop faster than the engine would be pulling it, you get a bit of a free braking effect, which can be useful for landing as well.
When the propeller pitch is set for high rpm (propeller lever full forward), the engine is operating at (or very close to) its maximum power rpm. Therefore if a go around is initiated, the engine will give its best performance.
If the propeller lever was set at a lower rpm, the full power of the engine could not be utilized, as power is simply torque x rpm. For example for horsepower the equation is torque (in lbft) x rpm / 5252.