Funnily enough I bought Squad recently and now I completely understand OP's points, Reforger feels far too flat.
There is clearly an example of suppression in Reforger, if situational: existing flinching animations for nearby explosions. These animations alone, adapted for suppression past our character's head, could do a lot of the heavy lifting for suppression, though in a more subtle fashion to align closely to Bohemia's stance on the mechanic (which I can half agree with, but there still needs to be an incentive to get into cover for the people who aren't roleplaying like their lives are in danger).