In answer to OP's original
According to Longman Dictionary,
"Why not" is a "spoken phrase" used to say that you agree with a suggestion.
My question is: Can I use Why not? in 'formal writing' as in the following sentence:
We then thought we might investigate whether an increase in the temperature resulted in a better yield. Why not?
According to Wordreference.com: Principal Translation why not interj informal (expressing openness to try [sth])
Compound Forms Why not? expr (why is that not so?)