How about using Powershell instead of creating linked servers to every SQL Server in your environment? I like the logic you have, a table with the list of servers, a table for exclusions, but using something as heavy as linked servers seems a bit over the top.

One other thing I prefer in my life, is an email regardless of success or failure. That way, I know that the "checker" is working. Relying on getting an email only if there's a failure is not a good habit for a DBA to get into.