Um, this is what the retina display does by default.
No, it simply renders at an effective 1440x900 resolution, but looks extremely crisp.
What I mean is if you could adjust the font size and icon size arbitrarily (like you can in Windows for example), you could have your 2880x1800 real estate and then scale up text to taste until it becomes readable to you. For most people you probably would not need to double everything back up to where it would be if you chose the 1440x900 retina resolution. So you would see an increase in useful screen area.
How can you make the font size bigger without making the UI elements that contain the fonts bigger as well?
For UI elements that contain non-scrolling text regions, generally speaking, you can't. But there are many UI elements (such as the text box I am currently typing this in) which don't fall into that category.