Come on guys, neither the Cheap Trick nor the Rockpile song crave for a 12- or 8-string sound. If anything the playing is a little stiffer than it would be on a 4-string because you can't bend strings as much and aren't that manouvrable/nimble on the fretboard, playing a multi-string is hard work after a while.
Lake's clanky sound is a matter of taste too, but it makes sense in a trio without guitar where there is no guitar for more percussive strumming, besides it's a style elment of a lot of prog music. I'm no great ELP fan at all, but on Fanfare that metallic bass sound fits the song. Mind you, Lake would eq his sound clanky with any bass he played, be it Jazz Bass, Ripper, Alembic 4 string or Alembic 8 string.
I've seen Cheap Trick twice in open air scenarios, it's incredibly hard to catch what Petersen plays. He has a wall of sound, but it's hard to pick out runs from what he does. It's as if his bass has a continuous delay running with it. It brings us back to the point that a multistring can sound awsome on its own, but clutters up the sound in a band setting and even begins to grate. In the ELP track all those strings at least have room to breathe because there is no guitar invading the mid frequencies.
But that said, I don't think the history of rock would need to be rewritten in the absence of multi string basses. I cannot think of a bass run on 8 string or 12 string that has introduced a hit song like McGuinn's 12 string guitar intro did on The Byrd's Mr Tambourine man.
I sometimes do get caught up in especially playing my Ric 8 String at home and it sounds gorgeous with effects in the solitude of my living room playing chordy harmonies, but once you are in the rehearsal room the guitarist really has to restrict himself for all that still to be heard.