I feel it's a liabilty to keep it online. Storing it offline is useful.
As in, I don't see the problem with having more storage - you use only as much as you want.
Personally, I find having all my mail searchable from any computer useful. And Google does provide lots of security features (2FA, suspicious login detection, new login alerts, login audit logs etc)
I really wish I followed this practice sooner as there's mail from the 90s I wish I still had. I've used e-mail continuously since 1991 so it would be a lot of mail. Disk space is the main reason why I didn't do it sooner.