Except for the Auto Upgrade feature inbuilt to SEPM, you don't need to remove the "Uninstall Password". Don't confuse yourself with the SEP password protection with Tamper protection. SEP password protection is designed to prevent user from accidentally/intentionally changing/Removing the SEP client, policies or the communication settings.
Whereas Tamper protection is designed to prevent other process/ users abusing/tampering the SEP client files,registry keys and processes. Please let us know if you need more information.