So I had an idea. Now, feel free to tell me I'm an idiot if I'm wrong, but is it not possible to beat the game only collecting the one mandatory treasure on the first day?

Think about it. You could keep grinding the first cave, collecting dwarf bulborbs until the debt is paid off.

You wouldn't even need to get purple pikmin. The whole game could be beaten with red pikmin only.

Has this ever been attempted? Even as a joke?

Well give it a try and report back. I don't think anyone else wants to do it right now but you are free to run whatever you want.

you can beat the game without a single treasure using day 1 extinction, but it would take hours upon hours upon hours, since you can get maximum 22 pokos per trip. one person has done it, it took them 16 in-game days, and keep in mind each visit is like 3 minutes and doesn't let time pass. you can visit the cave a good 30 times in a day. do the math. nobody wants to do this.

to save you doing math, it takes 455 trips to the cave. each trip is about 3 minutes, and it takes about 30 seconds to walk to the cave. add the 10 minutes of setup before entering the cave, and you have a grand total of... 1602 minutes. almost 27 hours.