You already can with opensource models. Its kind of insane how good they're getting. There's all sorts of finetunes available on huggingface - with all sorts of weird behaviour and knowledge programmed in, if thats what you're after.

Whould we be able to pick that PI == 4?

It'd be interesting if the rest of the model had to align itself to the universe where pi is indeed 4.

Square circles all the way down..

you can alter it with base instructions. but 99% won't actually do it. maybe they need to make user friendly toggles and advertise them to the users

Do you mean each different AI model should have a preferences section for it? This might technically work too since fine-tuning is apparently cheap.