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

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.