> The whole point of managers is that they're there to protect their engineers from getting off track with every random request that comes up. I understand that it may feel bureaucratic, but as an engineer, someone who insists on talking to me directly without going through my manager is always going to mark themselves as someone who doesn't respect my time and doesn't understand that they're not the center of my universe.

Yes. I don't have a manager at the moment, so I have to field these requests myself and my productivity has tanked.