Can you be bit more detailed about actual use case?
When application uses CEF to simulate other browser (for example, to show mobile version of website), it needs an easy way to change user agent both in HTTP headers and JavaScript.
So, if you have application similar to Chrome device toolbar where you can enable mobile view and change your device with drop down control, you have to recreate entire browser just to change 1 string in its settings. JavaScript navigator object is read only, so it is impossible to use JavaScript injection to bypass the problem.
Actually any automated web pages test framework based on CEF may need to change user agent.