For as long as the wheels are on the ground the upper surface of the axle is under compression.
You are right, the axle will flex. But when flexing the upper surface will go from relaxed to compressed, to relaxed, to compressed, to relaxed etc.
Under normal condition that axle would carry a static load around 700Kgs (guess), up to about 1100Kgs in a bump situation. If the wheels come completely off the road, and they will at times, then the axle is lifting the wheels and brakes which would be about 20Kg.
700 to 1100Kg verses about 20Kg.
i hope that makes sense.
Darren