At the personal level, it wouldn't be. It makes a lot of sense, and I do the same with Fastmail.
At the corp level where it's often in M365 cloud, you've got hard limits from Microsoft on one hand (100GB primary mailbox - period), and corporate data retention limits on the other. Legal often has strong opinions on how long you are allowed to retain emails which you may or may not be able to personally override. Could be just a few years, which forces a different strategy.
I'm not sure on the details of Google, but one imagines corp workspaces have equivalent interests.
Edit: We were on GSuite.
But I've seen enough corrupted PST files in my days to never trust Outlook/Exchange as permanent file storage.
Now with "New" Outlook you don't even get that, you get an ODT cache file, everything else is permanently server side in Microsoft land.
Enterprise "productivity" software is fundamentally broken.
Is this strange?
I'll be trying to solve some problem, half-remember an email conversation from several years ago on something relevant, and want to look it up.
This feels like the most natural thing in the world to me, and it's not like the ability to save emails is new. Why, exactly, would a forced change of habits be for my own good?