What we do is we start with actual kumite from around 5th kyu (green belt level). We spend a long time in kihon before going into contact training. There are certain steps between kihon and our jiyu-kumite.
Yakusoku-kihon-kumite: prearranged basic techniques,
Tangan-kumite: eye-training,
Yakusoku-ippon-kumite: prearranged one-attack,
Kakari: only attack, open guard may be tapped by uke,
Jiyu-ippon-kumite: one-attack free of choice,
Jiyu-kumite: (bogu) free attacks full contact. (
And Jigen kempo: multiple opponents. This format can have different stages aswell.)
We use this way to gradually adapt to being hit and hit.
The first to stages mentioned above will start at 9th kyu, the actual attacks (full contact, but controlled) only start at 5th kyu.
Green belts that put on the bogu and do kumite usually have three types of reactions.
First: the blind, vision turns 'red' and the slugfest starts, shinpan is hardly heard at this stage.
Second: intimidated, after the first knock they question if they want to do this (some stop karate from this point).
Third: Oh, so this is what they mean by getting hit, let see what I can make of this.

This last reaction is what we hope for in our students. This is the right attitude: do and learn. They will see it as training, not as 'blind fury'.