No momentum and cloud swinging aren't the problem by themselves, they're just the easiest way to talk about it. In SM2, you navigate the city by aiming a web at a building in front of you, then waiting for gravity and momentum to take over, then when the time is right you press the jump button to let go of the web. If you want to hang a left, you web a building to the left of you and let your momentum carry you around the corner. That's the most basic form of it, but as you go through the game you gain the ability to boost at any point in a swing, web-zip (yank yourself forward), wall-run, wall-jump, wall-crawl, do crazy acrobatics between swings, and from then on you realise you have such incredible control over what Spidey can do. You gain speed by letting go of your web at the fastest part of your swing, or gain height by letting go right at the top, and you're constantly sprinting along walls or bouncing between buildings just for fun.
Subsequent games cut out mechanics one by one, until Amazing Spider-Man came around where you hold the right trigger and point the left analogue stick. There's no swinging system there at all. The fact that he swings from clouds is totally irrelevant when he might as well just be a helicopter.