Someone is ragging on my beloved impis?
In my current game (emperor aggressive ai raging barbs), it's 600BC, and I've brought the three most powerful empires on my continent (two of them very distant) to their knees with a grand total of about 5 impis, while I was simultaneously fighting off more barbs than I've ever seen before. And those empires are never getting back up. My impis have also stolen about ten workers and escorted them home through miles of barb-infested jungle, killed a couple of settlers, killed a bunch of archers in the field that were moving to reinforce endangered cities, forced those empires to keep their units sitting at home rather than trying to attack my territory, kept my huge sprawling empire safe from immense hordes of barbarians, provided me lots of money from pillaged improvements, scouted out masses of territory, acted as healers, and a few more are about to help out as mobile happiness stations when I get monarchy. They even took out two border cities, which I thought was quite nice. The only downside is that three big wars (including the subsequent capture of a protective hilltop holy city capital with a couple of axes who came along later) have only netted me just over 20 great general points. Saves on the war weariness though
Game before that, a guy on the other side of the continent was about twice the score and power graph of everyone else at about 1AD, with a couple of archers and about 3 axes/swords per city (and he had a lot of cities), and was threatening to run away with the game. Sent about 5 impis at him, lost one, but his score flatlined after that and he was never really a serious threat again. Five axes or swords might have gotten me one crappy border city for a couple of turns until he captured it back and barely harmed him in the slightest.
If you're bashing impis up against decently-defended cities, then you deserve to get crap results out of them. That's what swordsmen are for. If you're just using them as escorts, you're wasting their potential. If you're using them to utterly destroy an empire's ability to function, while tying up their entire war machine with only a handful of units, then you'll find that there's no sweeter unit in the game. Its housekeeping and escort abilities are just a beautiful bonus.