The amount it could potentially "weaken" protection is likely negligible compared to how much it reduces the burden on the user (unless you consider the risk of having a single exposed password in plain text now means N machines are compromised instead of 1).

Anyway, I'd assume that each LUKS key slot has a unique plaintext salt to prevent a single rainbow table being useful to attack every key slot - the attacker would still have to build a unique rainbow table for each. As long as this is the case then the time to bruteforce a password should be the same no matter how many keyslots or machines use the same password.