He didn't go to cool off, they called him in there(to kick him out).
Supposedly Willie did hit Joe a couple of times. So you're really saying that they should have kept Willie in the house, after physically attacking someone(and making other houseguests feel unsafe, cause there's a guy in the house who can(and did) physically attack someone).
Imagine being in that house, knowing you can't get out, and stuck in there with someone who you know,can physically attack you at any moment.
It's part of the rules, and he broke it, so he was out. And what happened to Willie after he left the house(not relating to big brother), proved even more why he should have been kicked out, he did similar actions that he did in BB house, in real life, and got arrested.
multiple players have said he went to cool down but the DR didn't let him in.