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.