Both for the user and for the server/instance, it wouldn’t be wise.

From the perspective of instances, imagine having large instances (such as yours, lemmy.world, with almost two hundred thousand accounts as per FediDB current statistics) implementing a cron to compile and store a potentially large JSON/ZIP file for every account (including potentially inactive accounts), and having the storage requirements suddenly doubling (as the media files will become repeated twice in the server storage), which will make the storage quota/bill go through the roof for the instance owner(s) and/or, at best, having the Fediverse platform momentarily competing for storage resources with the backup cron. Notice I’m not just talking about the textual contents, but also about media (photos and videos) which should be included in the backup (otherwise the backup would be partial).

From the perspective of users, especially those who are prolific participants with thousands of posts, imagine having the instance pushing a large ZIP file into your browser’s (or phone’s, especially if you’re using a third-party app to access the Fediverse) storage every week or so, potentially in an non-consented manner, maybe pushing the backup media as new files so your gallery app (when in mobile environments) will get suddenly cluttered by potentially repeated images and videos.

Nonetheless, for most Fediverse platforms, the exporting feature is quite “automatic” already, as the backup file is often built in less than 10 seconds upon requesting it, but it only does so when the user requests so; given the unlikelihood that all users will request their backups at the same time, the backup feature (generally) doesn’t overwhelm the server, but it would if this automatic backup feature were a thing.