I have no issue with trIbute acts, they are everywhere. I mean even people not keen on such acts will have struggled to have avoided at the very least seeing an Elvis impersonator at a bar somewhere and many actIve bands also have fairly well known tribute acts.
For me the problem arises if LP decide to start touring with a new singer who will presumably not be a like for like Chester replacement. The band will sound a bit different meaning that for those fans wanting to see the bands hits performed as close to the original as possible HT might offer that more so then the actual band themselves.