There's one big drawback I discovered the hard way, to not storing emails locally.
If you have to leave an org for any reason, you lose access to the entire email history with that org. Some of which might still be important to you for a multitude of very legitimate reasons (such as contacts).
You're right about keeping an offline copy of emails - especially with the help of an indexer like notmuch or mu. But I'm not sure why you mentioned it here. In case you think that aerc supports only IMAP, it has good integration with local maildirs and notmuch. Somebody else mentioned that maildir support felt like a second class citizen. This was true during the initial phase of the project. But the developers changed their mind some time later (there's a blog post about it somewhere) and gave it a better UX.
Assuming by org you mean an employer - this is also a benefit. For legal reasons, you may not want to have a copy of any of those emails anymore, or at least your employer may not want you to.
I try to forward important e-mails to myself if I think I'll need them outside of work (insurance details, etc).
I'm not usually concerned with what the employer does or doesn't want if they've decided they don't want me.
> I try to forward important e-mails to myself
They'll invariably be aware of this.
Your employer doesn't have to know everything about your business with them. They may think they deserve to, but that doesn't necessarily mean it needs to be true for you.
One might argue that this is a bit of deception, but it's also self-preservation of self-interest.
If you have to leave an org for any reason, you lose access to the entire email history with that org. Some of which might still be important to you for a multitude of very legitimate reasons (such as contacts).