Web developers code to Web browsers, so bugs in Web browsers lead to sites depending on those bugs, making those bugs unfixable unless you have developers testing in multiple browsers. Spec bugs don't become unfixable that way.
“It works in Chrome” (and previously IE) is a real issue and the browser that broke compatibility like that would have to be supported (potentially through the coercive power of its own market share - see the initial “any open source browser versus IE is a good thing” switching to “we need multiple browser engines, even if they’re all open source”) by the others or face irrelevance.