You know how everyone says it's a massive plothole that Harry's name comes out of the goblet and they all just go "Oh well, guess you'll have to compete!" and don't bother just excepting him or making the tasks extra easy for him etc?
Well I noticed - Mr. Crouch is supposed to be under the imperius curse at this point, isn't he? Because his son is disguised as Mad-Eye Moody and doesn't want him to give the game away. When Mr. Crouch arrives in the Great Hall during the feast, he's described as looking "uninterested and bored". We're meant to think this is just his boring, Percy Weasleyish character, being all uninterested in fun things like games, only interested in boring grown up things like reports and regulations, but that's not actually right, is it? He helped organise the tournament and should have been interested to see who got picked as champion. He was interested at the Quidditch World Cup, before he was being controlled. Ludo Bagman is almost OTT excited which is in contrast so I think his lack of enthusiasm doesn't stand out as strange next to that, and you don't notice the difference between him being calmly interested at the world cup vs completely uninterested at the tournament.
But anyway - when they all go into the chamber and discuss what to do, they basically defer to Crouch because "He knows the rule book inside out" but if Crouch is already being controlled by this time, he will have been primed to expect this happening and instruct everyone that Harry has to compete, whether that's actually in the rule book or not. And then Moody appears out of nowhere to also back him up and everyone goes with that. They probably should have double checked, but the teachers wouldn't know the rules since it's their first tournament, and Ludo Bagman is always presented as being a bit haphazard and leaving the rules/regulations bit to somebody else.
So with Moody + Crouch both on the "Ensure Harry competes properly at all times" team that's probably why they go that way despite it being illogical.
As an aside, it's just starting to bother me that nobody ever explains occlumency as the reason that everyone blindly trusts Dumbledore's judgement until book 6, it would explain a lot - like Dumbledore immediately taking Harry's word for it that he didn't put his own name in, and why Dumbledore trusting Snape is a big deal (in book 1). They're all just like "Oh Dumbledore trusts him and I trust Dumbeldore" and not "Dumbledore basically has lie detecting eyes, so believe him"