I used to think that the different ratings for blitz/live/correspondence were a good thing, but now I really hate it.
I occasionally start a handicapped Go tournament. Inevitably there are disappointed participants giving huge handicaps to people whose correspondence rating lags their actual skill. Most recently, I asked a mod to fix some problems before the tournament started.
I’m worse at live games than correspondence and worse at blitz games than live. But most people are. If a poll were started today, I’d vote for just one rating.