After 20 years of working I've learned: answer quickly (to the emails that you intend to reply to) even if the only thing you can say is "I have read this and will get back to you".
I used to fuzz and wait until I had the ultimate, perfect reply.. usually like 12-48 hours later. Turns out that is the wrong approach - for the reasons outlined in this article.
> On the other end I commit to read every emails.
That was my defense too! I iterated it over and over to my team (my bosses would get preferential treatment...), but noone would believe me - unless I responded. People tend not to believe invisible things.