Okay, I finally am posting a picture...
Paul, I hear your point. The weed is not hard underfoot. The leaves are a bit waxy though. It does, in my opinion, look pretty ugly in the lawn, although you don't really notice it when it is mowed. Problem with that is that it is difficult to mow (many passes with the reel mower to actually get it - it kinda pushes over in front of the mower).
The big thing I'm worried about is having this stuff slowly spread through the whole lawn. It is definitely classified as a weed, but it is not on the alien invader list, so I couldn't use that as an excuse either
It is just generally considered a real pain, as it is difficult to get rid of. It is not indigenous (it is from North America, I'm in South Africa - my gran says it was originally brought in by florists).
Anyway, that is my story. I still want to get rid of it - its propagation method bothers me quite a bit...