I have had a very similar issue... across 3 computers (2 x MBP and one iMac), we have had mail constantly downloading since late November 2017. I reported this to Apple on the 4th of December 2017, and after speaking with many support staff at Apple Care, we still as of today (23 Jan 2018) don't have a solution.
For us, it's having a financial impact as we are going over our data allowance as we are using wireless 4G in our office, and in Australia, these are limited... you can't get limitless data with wireless 4G here. So far it's cost us about $80, but if it doesn't get resolved, it will cost us much more. Plus it's cost us the time we have spent trying to fix the issue with Apple. The issue is, Apple doesn't know how to fix it, otherwise, we wouldn't be here talking about it almost 2 months later.
For everyone's information... Apple tried to insinuate that it was a Google (Gmail) issue... I then discussed this with Google and they said that it can't be and gave me a number of reasons why it isn't their issue. The one thing that they told me to do to isolate the problem was to use the same accounts on a different mail client, and if the problem did exist after doing that, then perhaps the issue may be with Gmail and the settings. So I did the exercise and put all the accounts into Outlook for Mac... After spending about 24 hours syncing across all accounts, Outlook was stable. I then had both mail clients running for a few days and took screenshots of the activity monitor to show how much data was being used by each program. And I mean I took a lot of screenshots... close to 60 over a week. This proved the issue was with Apple Mail and not with Gmail.
After doing all this, I was told to delete all accounts from Apple Mail and to reinstall them manually (without the Google prefixed settings). I did this and again after it fully synced, we keep having the same issue.
So 6 days ago (17 January 2018), I again contacted Apple via email asking for them to call me or respond to my problem, but as yet, I have not had a reply.
Does anyone know what's going on? lt's obvious that Apple doesn't know how to fix this right now, so I guess I'm reaching out to the wider Apple Community.
I'd be grateful for any advice.
Thanks 🙂
