Any idea how guitarists remedied this problem with real amps? For example the horrible Marshalls?
I'd just like to emphasize what DonPetersen said about compression. When you can't turn it up to 11 to crush the transients in the amp, a properly dialed in compressor can certainly help diminish the pick attack. As Don pointed out, the pick sound comes from your transients.
If you turn the compressor's attack to as fast as it will go, you're telling it to engage immediately (or as immediately as the compressor will allow), instead of waiting a few milliseconds to allow an initial attack to get through before you clamp down on the rest of it. This is what happens when you crank a Marshall so loud that the power amp section compresses. Conceptually, it's doing the same think - lopping off that initial spiky attack, and that's the part that's bugging you.
I would recommend sitting down for a session with the Kemper where you take a Marshall that you particularly don't like (in this regard), and then going through each compressor one at a time. Go into the dials and set the attack to the extreme - as fast as it will go - to see what its maximum capability is for taming this, and how it feels to you.
The release parameter, by the way, says "how long do I keep the signal clamped down before you want me to let go of it?" A very fast attack and a very slow release will keep it continually compressed without letting up. A fast attack with a fast release will create what's known as "pumping" where you can really hear it clamp down the signal, let it back up really quickly, then clamp it down on the next note, etc. That's often considered undesirable (but has its applications in things like EDM).
So, first max the attack to see what it will do for you, but also be mindful of your release. Walk through every compressor in the Kemper, and I think you'll find that you have a lot more control over the "pick-iness" of the Marshall (and other) tones.
Ultimately all that matters is what sounds good to your own ears, but when going into battle you get fewer nicks and cuts if you actually know how to use your weapons.