This is what escalation is for - the job of a VP or Director of Engineering is to decide what is actually urgent and approve fast-tracking it, and what should actually follow process. Having an efficient escalation process is critical.
Very much this: there should be a process for "emergency change" and that process has to be used for every actual emergency and not for anything else.
I've found that those in charge also have a budget to run you on... how do they justify you spending x hours updating code to do exactly 0 as far as anyone is concerned? ..plus all the regression testing?
They just don't... it gets left as it is