I don't see that a LOMC would be quieter because of its lower output - which will just be amplified more further down the chain to end up with the same volume at the speakers. However, some cartridge designs are said to be relatively insensitive to surface noise, though I find that an odd proposition (if a chunk of crud in the groove is big enough to make an audible sound with one cartridge, presumably another where it does not make such sound must imply the second cartridge is missing other details in the groove?)
As for keeping records clean, that is a duty for all of us. But having cleaned and used a new inner sleeve, it should be good for many plays before cleaning again. Could it be static that you are hearing?