I ran through all the then-current emails and archived the rest. I also signed up for Boomerang to permit to (a) have an email return to my inbox at a set time and (b) delay email sending to a scheduled time. Both are great features.
It has gone well. I have 12 emails in my inbox right now. All require action. I have recently been traveling and permitted my inbox to grow to 89 emails, but it took all of 5-10 minutes to sort through them and archive those which required no action. The move also permitted me to look over the prior work and determine what, if anything, required additional follow-up.
Down sides? I don't see any. Before, I never looked through my older emails except via search because there were too many of them. I am more likely to just run through the historical emails now because they are manageable. I don't have a case of purging an email I wish I had kept. It hasn't happened yet.
Wanna do it?
1. Make sure you have a good, stable place to archive emails.
2. Read your last 100 or so emails. Keep the ones that require action. Archive everything else.
3. Make it a goal every day or week to get as close to zero emails in your box as possible.
4. Consider a tool like Boomerang to help you.