How does a painter know what to charge?
Then they will adjust the price based on how much extra work they anticipate. Heavily pigmented paints take more work. Do you need a primer coat first? Your opinion only counts if you won't hold the painter accountable for the finished product and no painter will trust you on that issue. They've been burned before.
An established painter uses his/her experience. They just know how long certain rooms take.
Why would you expect someone to bid a job blind? There's no way anyone can tell what shape your walls are in. The walls and/or trim might need extra prep.
You might have a lot of furniture to move around. Some spots may take special scaffolding.
Bottom line - its not just the square footage.