Hundreds of thousands of emails in your inbox has absolutely nothing to do with IMAP/POP3, its how you manage your email.
Install one of the free mail clients, configure it as a POP3 account and download all the mail to your device.
Bear in mind that creating a POP connection and downloading mail will only archive what's in yout Inbox, not subfolders, or Sent etc.
Some mail clients have an export or backup function, which will export all your mail to file, but it depends what mail client you're using.
Thanks liquorice, HolmPC.
I have Outlook 2016, which is what I think you mean by a 'mail client', but that has been presenting its own problems, so much so that I have stopped using it for the time being.
I would indeed want to archive subfolders; I tried this once in Outlook 2016, but it just seemed to create another subfolder, labelled 'Archive', without reducing the number of emails in the account, the whole point of the exercise.
Suggestions gratefully received...
If you have Outlook 2016 then all your mail will be stored a .PST file on your PC. If the account is configured as IMAP all the folders will be included in the file.
Not sure what you are actually trying to achieve, I thought you just wanted a backup of your mails. If you want to reduce them you obviously have to delete them.
Haven't got Outlook 2016, but in Outlook 2010 archiving just creates a new data file (.PST) which appears as Archives in your list.
If you don't want the data file to appear in your list, just go to account settings , select the Data file tab highlight the Archives file and click remove. It doesn't delete the file it just removes it from the list in Outlook.
I backup my emails with MailStore Home for Windows - it is free for home use and easily backups all emails (and all email folders) to a central archive on your PC or external drive/device where you can quickly find, sort or retrieve them. Works with Outlook, Windows Mail, Gmail and multiple accounts. I find that running it once a month suites my needs... https://www.mailstore.com/en/products/mailstore-home/