Currently, all Esri self-extracting downloads default to the user's Documents directory. The user can change this, but the default is essentially My Documents. My view is that a user's Documents directory is precisely for that: documents. That folder should be where word processing files, spreadsheets, maps, and code reside. Many people back up their Documents folders via OneDrive, Google Drive, Drop Box, and other automated tools. Backing up full Esri installers that can be easily downloaded again from your web site seems to be a waste of space.
My idea or suggestion is that the self-extracting executables default to the user's Downloads directory. That directory is treated differently by back-up tools and some backup tools even ignore it. Users that routinely copy their Documents directory to file servers, external hard drives, and cloud storage won't be wasting any space by copying Esri installers to these locations. The self-extracting exe is likely already in their Downloads directory to begin with since the most popular browsers use this path for storing downloaded files from My Esri.