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Here's what I use, albeit on a much lower number of sites.

All of the sites are backing up to Amazon S3 using the native CRON script method. The CRON daemon can optionally send you the output of the command it runs by email. In cPanel, it's as easy as typing in an email in the email box and clicking Submit.

Here's the tricky part: knowing which sites have backed up, which haven't and which backed up with errors. First, we can assume that CRON itself either runs or not. It's a system-wide service, it's been around for decades (yes, it's that old), so the command "not running at all" is not something to worry about. Therefore, we are left with two possibilities:
a. The CRON job runs to successful completion, or
b. The CRON job runs but, for whatever reason, fails
Industrial automation dictates that if there is no error, do not notify the operator (saves the operator from excessive feedback which would make identifying an error condition impossible). Extending that principle to site backup, we would ideally need to be notified by email if and only if a backup fails. That's easy, with mail filters!

Every successful backup prints at the first line something like "Akeeba Backup CLI svn563 (2011-04-16)" and at the last line something like "Backup job finished successfully after approximately 3 minutes". So, we need three rules, in the exact following order (if the first matches, the other should not execute):

1. Successful backup. The message body contains "Akeeba Backup CLI" and "Backup job finished successfully". In this case, trash or move to a folder for safekeeping.
2. Backup with warnings. The message body contains "Akeeba Backup CLI" and "POTENTIAL PROBLEMS DETECTED;". Move it to a mail folder named "Backups with Warnings".
3. Failed backup. The message body does not contain "Backup job finished successfully" and the sender is our CRON daemon (in the case of my site it's something like [email protected]). Move them to a mail folder named "Failed backups"

This way you have your realtime report of backup statuses per domain in a convenient email format. Moreover, instead of having to spot which one of your 100 sites did not email you about backup completion, you only have to spot which one did mail you about a problem. Ta-da! Simple and sweet :)

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