It is possible xp_readerrorlog could either be resource intensive if you have big log files or cause headaches once in a while.
If you are trying to be proactive, you may want to look for other options like a monitoring software that will notify of general failures and even error log failures. I don't know if these use xp_readerrorlog though.
If there are xp_readerrorlog stack dumps, you may get notifications of these errors in the email that your own xp_readerrorlog caused. :-P
Also, it is common for some (discontinued, mispointed) applications logins to cause thousands of login failures, etc. You might need a different email account if you are positive of this method.