Not to sound condescending, your tractor doesn't "know" if the PTO shaft of the cutter is attached.
Since this is totally a hypothetical discussion I'll add this.
The PTO clutch is a wet clutch, meaning it's running in oil and is activated by oil pressure. If the activation mode is softened the clutch discs will slip longer before complete engagement is achieved. So, wouldn't this slippage cause premature clutch disc failure?
No condensation taken, and never would be. To me, there is no such thing as a bad thought when we are trying to contribute to a solution. And agreed with respect to the electrical circuitry. That is why I couldn't understand why the tractor wouldn't start after it shut down following a violent PTO engagement. I turned the PTO electrical switch off, on and off several times. No go. So, I wondered if there were a mechanical component to the "all is clear" electrical circuit. Stated differently, I thought that if the PTO shut down suddenly, there might be a hydraulic pressure feedback loop or some such to prevent the tractor from restarting when there was a problem with the PTO. So, I disengaged the mower PTO shaft from the tractor PTO, and the tractor started. I don't know why this worked, but it did. I haven't investigated it but to me a logical possible answer is that there may be in the PTO-engagement circuitry a pressure-sensor switch that senses when there is still hydraulic-oil pressure trying to rotate the PTO even though the electric PTO engagement switch is turned off. That's why I tried disconnecting the mower PTO shaft and rotating the tractor PTO shaft both ways. It worked, but I am for sure not saying that the reason is what I thought it might be. Interesting, though.
Another good and pertinent thought. Based on my limited experience to date, I would probably run the risk of premature failure of the discs in order to eliminate the violent PTO engagement of the attachments, especially with the mower, which is my most often used attachment that requires the PTO power.
I have a Massey Ferguson with a similar electric PTO clutch. Starting my brush mower....it is almost scary given how bad it sounds. In contrast, starting my PTO wood chipper is about as smooth as can be. Go figure.
I'm afraid that's the nature of the beast. Do your engagements at engine idle to minimize the shock to the cutter or any other PTO attachment.
I think the reason the rotary vibrates when it starts is that the blades are swinging on their pivots, which means the entire assembly is unbalanced. It's made to be balanced when the blades have swung out to the farthest position, not when they're swinging back and forth like a pendulum. A slower start like you can do with a manual clutch would reduce the pendulum effect.
Same applies to disengaging an implement...idle down for 5-10 seconds before disengaging the PTO. Makes for a much smoother transition and, undoubtedly, will extend the life of the implement and tractor.
On really old tractors, you could disengage the clutch to take load off the engine but of course the PTO and transmission would still be coupled. It was possible for the PTO implement to then keep driving the tractor forward if it was in gear!! I am sure that caused some pucker moments.
I think it depends on the type of PTO (live, etc), type of clutches (main, overrun, etc) -- if the implement has a heavy flywheel or flywheel action, that easily can overdrive the PTO and transmission/engine after you throttle down. For example, on my wood chipper, it's far better to disengage the tractor's clutch, then throttle down, then wait for the chipper to stop spinning the PTO and transmission before finally disengaging the PTO. If you just throttle back, the chipper's flywheel inertia could over-run the engine and transmission if there wasn't some sort of over-run slip clutch.
Anyone that engages a PTO driven implement at full PTO RPM probably needs to review the owner's manual a few more times.Here's a suggestion the OP can try. (I am sure the safety police here will jump all over it though). The whole problem is that you are up against Newton's 1st law, which is an object at rest tends to remain at rest. There is about 150lbs of mass that is sitting perfectly still, and all of a sudden you are trying to make it turn at 540 rpm's! Hence, it is creating a big shock to the driveline when the PTO is engaged.