The obstacle course had no rules other than staying on course right? Why didn't Todoroki just freeze everyone in the tight tunnel starting area..? Sure, he might accidentally kill some of them, but the teachers are there to save them before too many kids die. At least that filters most of the contestants.
Izuku winning with no powers was nonsense, but that has been consistent with the rest of this show. I've always complained about how events are logic defying and don't even follow the rules the story sets for itself (Insta-heals, Bakugo fight, and now enduring explosions that can throw you hundreds of feet), but I have come to accept this as the show's style. It's not an oversight but a willing sacrifice to make cool and heart-pounding scenes, and as long as it is able to achieve that, I can overlook it.