The Kickr Core is a stiff little unit in my experience. On concrete you can feel the bike frame flexing under load.
I have various bikes that I’ve used on the trainer and my aluminium frame has the least amount of noticable flex.
Carbon bars flex and I’d consider that a good thing. Likewise, the carbon frames tend to flex, but mainly around the contact points.
The down tubes and bottom brackets are stiff as.
Buy yourself a foam yoga block and cut it up to make supports for the legs if you want the Core to move a little more.