The title says it all. Could StackOverflow have the ability to insert "inlined code", as well as change the format of code blocks to be the browser's default monospace font?
You can already insert in-lined code using backticks,
like <this>. Do you mean you want syntax highlighting on it? If so, I disagree. That would be remarkably distracting.
This is a test of
x + (y + z) == (x + y) + z
(Use ``, if you want syntax highlighting, use a code block.)
They will not use browser-default monospace font because Webkit-based browsers treat them differently than all the other browsers.