I'll grant you that if they have to choose, they probably choose total productivity over all emails answered. However, clearly not every incoming email requires an answer from every recipient. You are not being asked to reply to 100% of incoming emails instantly.

Ignoring direct requests for attention is both rude and in my opinion ultimately toxic. Imagine what would happen if everyone acted that way. It blocks information flow, holds people up, and ultimately doesn't solve the problem - you are just forcing someone to follow up some other way. It actually hides problems. Those can be that you are doing something wrong: poor at organising your email or your time compared to others; contiually optimising visible productivity at the expense of other people's time; poor communication skills. On the flip side, it can be that the company has poor email culture, suboptimal team structures/dynamics or just too much work for the number of employees. If your manager met you by the coffee machine when you were busy and asked you for something you wouldn't just walk away.

None of the best or most productive people I've worked with have been casual about dropping 40% of their emails.