An electrical safety test with no electricity involved what a perfect way to make sure everything passes and is "safe".

Well, if you read IEC 62353 you would know the Alternative method tests apply an AC voltage equal to the mains voltage to perform the test. So we do indeed have electricity involved!
Think of it as a souped up insulation test, except you never get the same reading (infinity) with the DUT either plugged into the test meter or not! You get a accurate representation of the true device leakage, which is directly related to the 60601-1 open neutral value.
Also not many test meters I know can switch from performing equipment leakage tests to applied parts leakage tests without interrupting the mains supply to the EUT.