Why does it mean that these accounts are important to you but you don't sign in? I suppose perhaps there are sentimental reasons but in that case you might as

Why does it mean that these accounts are important to you but you don't sign in? I suppose perhaps there are sentimental reasons but in that case you might as well do a takeout, download everything, and enjoy whatever is in your account locally. On the other hand it's extremely easy to satisfy this sign-in requirement. Just set up a mail client that fetches Gmail over IMAP; you don't even have to read any emails.