Not parent but I have a similar setup.
Yes, absolutely. I think storing our owns emails/attachments locally is part of best practices.
That is our data and having a safe backup of it is a must.
Care to elaborate on the safety of backup? You mean it’s safe at your hard drive from availability or from privacy perspective?
Safe as in: "{random_provider} locked me out from my email account and I lost all my emails and attachments."