It's not possible to add this block to the Logs page.

Replication steps:

1. Log in as admin
2. Navigate to the Site Home
3. Ensure editing is turned off
4. Navigate to the Logs page using either:
   • Site pages > Reports > Logs
   • Settings > Site admin > Reports > Logs
5. Click Blocks editing on button (Not "Turn editing on" link from navigation)
6. Attempt to add a block

Expected result: You should be able to add the block

Actual result: Nothing is added, the editing mode turns itself off

I couldn't find another page that has the same behaviour. I would have thought that the Statistics report, which has similar properties, would be the same, but it is not.