The only problem with putting cigarette butts in a bin is that they're usually still smouldering when smokers are finished with them - meaning that simply dropping them in the rubbish isn't so much a responsible way to discard of one's waste, as a quick and easy way to set a bin on fire. This is the main reason ashtrays exist.
The best way to extinguish a cigarette is to crush it underfoot, but then few people are willing to pick it up and get rid of it properly.
Plenty of bins out on the street now have ashtrays in the top. Plenty don't. If the choice is between dropping a butt on the street or burning a bin, it's more logical to drop it, rightly or wrongly.