Rick, I'm not being a dick when I type this - I am here to learn but also impart correct information based on my knowledge. I hope you don't take this the wrong way as it is meant to be constructive.
Just think about these two problems in piston engines for example:
(1) The intake/exhausts valves for each cylinder - at say 6000RPM, the number of open and close is huge. The acceleration and deceleration of the valves are huge! (push up to open, relax, pull down to close). And each valve literally crash back onto the valve seat, each time! Each valve needs to do that twice per cycle.
Emphasis by me.
The acceleration and deceleration is close to sinusoidal on the open stroke and close stroke. Piston engines have valves which are forced open by a camshaft but are "pulled" back into the closed position by rather strong springs. They are not forced closed.
The transition between opening, open (stationary) and closing is somewhat less sinusoidal and is the most aggressive point of the cycle but far from "crashing" as you stated. I also note that you hint at the point at which the valve closes being the "crashing" point. Often the upper speed limit of a particular engine is set by the strength of the valve springs* - there is a fine balance between making the moving mass of the valves as low as possible and the springs very, very stiff in order to get them to close quickly and follow the closing profile of the camshaft at high speed, and reducing the parasitic friction of the valve system down to an acceptable value. The stiffer the springs, the better the valves follow the profile of the camshaft at high RPM, however the parasitic drag of the valvetrain goes through the roof and you end up using more power to drive the valvetrain than you gain by closing the valves quickly.
*It is as equally often set by the maximum inertia of the pistons and the shear strength of the gudgeon pin, which is normally made of something quite exotic and very, VERY hard. Included for completeness.
It does not matter what the absolute rate of acceleration (inversely deceleration) of the valves or anything is. As long as they are designed to be strong enough, the design is adequate. These design challenges are present within piston and Wankel types.
There is also a point whereby the exhaust valve does not follow the close profile of the camshaft at high speed, thus resulting in a less than smooth transition between the spring closing the valve and valve being on its end stop (i.e. closed) as the camshaft is no longer modulating (or moderating) it. This is engineered deliberately in order to break up the "coke" deposits left by normal operation.
(2) The piston connection to the crankshaft suffers a shock of an explosion each cycle. Goes super compression to push the shaft.
The burn inside a piston engine is fairly tame and is not really an "explosion". It is subsonic - the correct name is "deflagration". Both Wankel type engines and piston type engines have the exact same burn characteristics as the fuel and stoichiometric ratios are the same. The forces are imparted to the crankshaft in the same way - close to tangentially, therefore piston engines suffer no higher peak forces when compared to Wankel engines. If anything, the Wankel engine is susceptible to higher peak loads as the bearing loads of an entire chamber burn are spread over only one tooth of the central gear. Gears tend to have load areas closer to line contacts, as opposed to approaching half a circumference of a typical connecting rod.
Rotary engines has no piston, no valve, no crankshaft, etc, etc... None of those problems exist by design. But for the heroic effort in engineering to overcome piston engine's poor design, cars might not have came into being.
Rotary engines have one piston per "rotor". The rotor is the piston.
Some steam engines have no discrete valves - the piston forms the valve. This does not mean it has no valves, as valves of any description naturally exhibit loss.
Wankel engines have a crankshaft, it is just not traditonally "cranked" and instead it has gear teeth cut onto it.