All communication is a massive, productivity destroying distraction when you're working on something.

Structured tools are designed to organize and control communication into channels that are designed to handle when and how you deal with different things. Email is not, and bad tooling doesn't come close to closing the gap.

He's throwing a tantrum over the perfectly reasonable "we have structured communication tools; email is not a legitimate way to contact me", and pretending forcing them to use an alternate, bad tool is somehow doing them a favor.