My inbox is effectively one of my to-do lists. Since I don't cross off everything on my to-do list each day, my inbox usually has a few dozen messages. I have found that when I move an email to a "check later" folder, I never do so.
pg has described email as a to-do list of tasks assigned by other people.
The social dimension is my reason for pursuing inbox zero. Especially as a founder, it's important a) not to be a bottle neck and b) to respect others by responding promptly.
I'm similar to you in the to-do list inbox, and I also never check "check later" folders. Instead, I use Mailbox app (Boomerang also works for this) to "bounce" emails back into my inbox when I don't need them today. This allows me to hit zero each day and conveniently reminds me of important things at the time that they need to be addressed.
You need to get into the habit of checking your TODO. I find it quite easy to get into that habit with Andreas Klinger's system, but I haven't been able to with any other system I tried. I think it's because I see them on the right.
My inbox is effectively one of my to-do lists. Since I don't cross off everything on my to-do list each day, my inbox usually has a few dozen messages. I have found that when I move an email to a "check later" folder, I never do so.