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Yeah. I felt like the spirit of the question was about how moving water can rapidly stop without breaking energy conservation, so I focused the answer there. I did mention reflection back into the sea at the end.
How do you mean? Waves carry significant energy, but moving water carries even more significant cooling capacity.
Dam spillways are designed to dissipate the full power capacity of the dam with splashing, and there are modifications made to some shorelines to increase the amount of absorption of incoming waves, specifically.
My point is that the moving water doesn't "rapidly stop" when it hits the beach. The beach does not absorb very much of the energy of the wave at all.
As it arrives at the beach, the water flows uphill, against gravity, converting kinetic energy into potential energy, not heat, at least not in any significant quantities. Now the water is high up on the beach. Gravity drags it right back downhill. That energy travels back out to sea. Virtually all of the energy of the wave is reflected back into the sea. The proportion of the wave energy that is converted to heat/noise at the beach is a tiny fraction of the total wave energy.
The video I linked discusses mechanical wave energy absorbed by a "dashpot". The dashpot analogizes conversion to heat. If we were to model a beach, we would need to use an infinitesimally small dashpot.
Sure. I don't think we're disagreeing on much of any substance here.