the reason people feel ranged is broken is becuase their army ratios between melee and ranged. What's ideal, 3 ranged for every 1 melee? and do you use the melee for anything other than grabbing cities andmeatshields for the ranged?
I've definitely fought wars (depending on circumstances) where I have one melee unit that tags along to grab cities.
But, personally, I feel like calvalry is more broken than ranged. I get that it *can* be useful, but it is not needed at all, that just doesn't feel right.
Increase your difficulty and try spamming ranged. Suddenly the AI has Cover I on every unit, even their Warriors, and ranged alone are useless. You NEED melee units and Cavalry, ESPECIALLY if your neighbor is Attila or Ashurbanipal, because their siege units will start with Cover II, and horse units are the only things that are fast enough to flank the ranged they bring. I tried spamming crossbows when Genghis was my neighbor, and he charged at me with about 15 Cover I Longswords and 12 Keshiks. I couldn't kill those Longswords if my life depended on it, if I focus fired on one with all my crossbows, I might ALMOST kill one, so his Keshiks were nice and safe. I started spamming my own longswords to protect my crossbows and finish his off, and it evened up the odds, but it was too little too late. I would kill one wave and another would take its place before I had time to heal. He ended up wiping me off the map in true Mongolian fashion.
Cavalry is FAR from useless. Nothing kills ranged/artillery/AA units more effectively than Cavalry and Tanks, and nothing spots for bombers better, and thanks to all the cover I, and for the Charge promotion, nothing kills wounded units better. In fact, I think Cavalry is better than Riflemen for taking cities, Riflemen are just better for soaking hits and preventing the enemy Cavalry from charging the back line. If you don't bring enough rifles, I guarantee you that your ranged units will get mulched by a cavalry charge. For support roles, Cavalry units also make the best Medics.
I seriously have no idea what game you guys are playing where melee units are useless. Melee units do way more damage than Ranged units, are always the first to get their combat strength upgrade by a mile, and once melee units close the distance, the ranged units are toast, especially if the melee have Cover. The only thing melee units are worse at is attacking cities, but try bringing just one melee unit to a war and see how that works out for you. The AI will focus fire the melee unit and now your whole charge is dead on arrival. You need to surround the city with fortified melee, pound it with ranged and siege units, then use melee to make the final hits. DON'T FORGET TO PILLAGE! Pillaging gives you +25 HP, a bit of gold, and only costs a movement point. If you're about to move into rough terrain or through the city's ZOC, there's literally zero opportunity cost.
Oh, and Infantry units and Marines can learn Siege, which makes them actually quite good at attacking cities.