I'm very annoyed by people who don't respond to your emails because their inboxes have two thousand messages in them. If thirty messages come in after yours arrives, your email falls below the first screen, and is never seen again, because mail never leaves the inboxes of these people, and there shall be no follow-up.
I try to keep only three or four messages in my inbox at work. I use a color coding system to keep track of them. Unread mail is white and sorts to the top, unless it's from an important person, in which case it's black. Mail I need to respond to soon I flag red, mail waiting on other people is yellow, mail that I just have to deal with sometime is green, and everything else is either irrelevant to me and deleted, or has already been dealt with and is deleted or archived.
I never miss emails, I always respond quickly, and I essentially never forget an issue. The system is extremely easy to set up and maintain, and not once have I ever even considered that an extra click for each important email was not worth the time. I wish more people didn't suck at email. But most of these people don't really care about missing a few messages. It just annoys me when my email goes unanswered. It makes communications unreliable an inefficient, and I place a high value on communications. And yet I'm terrible at dealing with people who work this way. It's something I've been trying to work on for years now.