The one thing that would bother me about (some) carbon rims is them being too stiff when you’re cranked right over in a turn and the suspension can’t work at its best.
If you look at other 2-wheel sports like moto GP the relationship between stiffness and flexibility has been explored a bit further. When leant right over the suspension isn’t really pushing you into the grund, more allong it, which is bad, it means the line you think your taking round the corner isn’t the same radius for your COG and the tyres, if you botttom out at the apex then your mass is doing a sort of squared off corner while the wheels percribe a nice arc. Generaly it’s bad as that means the wheels are most loaded latteraly (suspensions most compressed) just when you need some more grip (which is generated by the vertical load on the wheels). But with the suspension working almost parralel to the ground it’ can’t track over imperfections in the surface.
This is where the stiffness/flexibility comes in. You actualy want the headstock (headtube) and of the bike to flex sideways a bit to give it some movememnt at the wheel. Make the bike too stiff and the wheel won’t be able to move and will just lose grip.
In MTB’s it was suggested that this was one of the reasons why the Cannondale Prophet became a cult bike, despite being reviewed badly at first for the flexible rear end. That added flexibility probably contributed to it’s reputation for being stable in corners as much as the low BB and slack head angle did.