Why? How? They actually can be stowed on deck.

They stick out the back a bit. I've more than once been stuck hanging between two rocks bow and stern. Sometimes you back into rocks, other times there are overhangs. A rudder is a mechanical piece sticking out in a high impact zone. Stowing on deck is fine if you never ever make a mistake, but that really isn't what rock gardening is about.

Playing around in a shore break you may stuff the stern into the bottom while back surfing. Pirouetting off your rudder pintle isn't what they are designed for.

Ease off on the side loading then i.e. steer gently back on course. What you really mean is you always broach on steep waves?

On large, steep waves, you often want to run on a diagonal to avoid over accelerating into the wave ahead, maintain control, flatten out the apparent wave angle, gain speed and link onto other wave trains. This requires a constant steering force to hold the line between straight down and swerving off into a broach. Even though your are striving to flatten the wave shape by running a diagonal line, your stern may still rise and your rudder come free of the water.

When the rudder lifts out of the water, there is no loading on the rudder - side or otherwise - but if you were using the rudder to maintain a line before it lifted, chances are that there was some side force on the boat otherwise you wouldn't have applied a rudder angle. Instinct usually means you will continue to hold that rudder angle until it reengages. You can use corrective paddle strokes/ruddering to get you back on line, but you installed a rudder so you wouldn't have to do that. If you fail to regain control with your paddle, chances good you will still have the rudder angle set as the rudder descends back into the water because you are still not running the line you desire. You learn to anticipate the sudden bite of the rudder, but it is one more thing to deal with in a dynamic situation.

I am mostly talking about surfing long downwind runners before broaching but this can happen in all kinds of situations. The amount of tipping torque created by a rudder is noticeable when going 5 mph (8 kph) and significant when you are moving at 10 mph (16 kph). You don't notice it that much while the rudder is continuously engaged, but having popping in and out is annoying at the very least.

Again, I am not anti-rudder but they are not the ideal solution for all people in all situations. It depends on the type of paddling you like to do. Most of the paddling I do, I don't need a rudder. For the paddling I do where I would like a rudder I haven't had the time to build myself a boat that is designed for a rudder. I wouldn't put a rudder on a design like my Petrel because it really wasn't designed to work like that. I would have better results using a design specifically intended for rudder from the start.

My surfski paddling buddy did put a under-stern rudder on a Valley Pintail. He really liked it, but I think it ended up breaking off.