Is there a reason it is not "kan godt lide alting", or is this just something that has to be rote learnt?
"to like" is literally "kunne lide". This "godt" makes it stronger, but it isn't necessary.
To me, "Kan godt lide alting" just sounds weird. "Kan godt lide" sounds like something that you really do have a positive interest in, something that makes you happy. It seems that "kan lide" sort of means that it just goes well with you. Don't take it from me, though. This is just speculation. An actual dane would know better.