What you are taling about with key 'clicks' etc, is the rise and fall times of the keying circuits. There are various ways of 'shaping' those timing 'slopes' so that you can't hear the objectionable 'clicks'. That's done in all CW transmitters, not just amplifiers. How 'much' is done also varies for several reasons ranging from it just wasn't all that objectionable to start with, to a totally over done 'shaping' circuit that covered every imaginable situation. It's a very common thing for other 'on/off' or pulsed modes such as radar for just one example. Get ready to learn more than you ever wanted to know about 'RC' timing circuits
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The reason you don't see that much CW 'plate keying' is because the key was 'hot'. As in plate voltage present. You only made that mistake once, and remembered it forever. Also why there used to be 'covered' keys. You could still get the snot knocked out of you, but it was harder to do, sort of.
And no, I ain't no "hard core CW op". Once upon a time maybe, but that was a lot of years ago, so I don't qualify.
- 'Doc