Aren't you thinking about this backwards? Of course the Apollo Familia people would be happy that Hestia accepted the War Game. They expect to win, expect some entertainment, and they also get to stop trying to capture/kill Bell.

They know attacking and harassing them on the street is wrong. They don't want to start a street war with the other Familia either.

So who isn't happy? Hestia, Bell, and that asshole who is Apollo's current ace.

Nothing is really out of place, or out of character for the setting, like you're trying to express.