As part of security best practices, I recently updated the password for the Initial Administrator account for our ArcGIS Enterprise Portal. The password contains special characters. However, there is a character limit restriction (ESRI documentation hyperlinked) which prohibits using special characters in passwords specifically for the Initial Administrator account. Any other administrator account does not have this restriction.
The impact isn't as severe though from my observations. Occasionally, one might encounter the "Too many invalid logins. Try again after 15 minutes error".
Proposed product enhancement: Do not accept Initial Administrator account passwords not adhering to the character limitations.