Hard CC is only necessary when your facing enemies who can deal lots of damage quickly or can sustain themselves in fights, otherwise slows can work fine.
This does not stack up with my experience of the game at all. Perhaps it's different in platinum and diamond and hard CC becomes much less important, but from what I've seen up to gold, hard CC is very, very important.
As the others have said, tanks and CC monsters (Sejuani springs to mind, filling both roles) would wreck that comp.
This exactly. That enemy comp you just described is exactly what I'm talking about: they've got a couple
single-target hard CC abilities, but they can't lock down an entire team. Sejuani was also the first thing to come to my mind. With that comp you described the buildorder is obvious: SV -> mercs -> Banshee's -> Randuin's to deal with Cait -> Warmogs -> Abyssal -> Dive your entire team, lock them down, eat all of your spells while my team unloads from a distance.
The comp you're getting at is literally the definition of what tanks like Sejuani and Nautilus exist to wreck, because they can either engage on your or wait until you engage, CC your entire team for days, and then let their team pull cleanup duty once you've shot your load. Your alternative, of course, is not using abilities on them, in which case they ignore your puny AAs and kill your squishies.
Remember, Sejuani's kit is literally this: Passive = Bonus armor and slow reduction when damaging enemies, Q = Gapcloser + knockup that does %health damage, W = AoE damage that scales with bonus health and applies the E passive, E = Passively applies with all abilities and basic attacks, active burns marks on all marked targets for damage and a massive slow, R = Long range AoE stun with a wider range of AoE slow, even if it doesn't hit directly.
She's ideal for dealing with this sort of comp, but anyone who can get into your team and lock them up is going to wreck your initiates, especially if they have a teammate with AoE hard CC who can follow up, or a good multi-target damage ult. No one comp is perfect or uncounterable, and heavy CC/an aggressive tank happens to deal with monodimensional threats like this one.
If Karthus dies before he can dive, if Hec's engage is blocked by the enemy tank, if Kat is knocked out of the fight before she can engage, if the fight pushes the enemy team away from Cait and her damage, if Fiddles (like Karthus) is locked up and badly hurt before he can dive... basically, if any member of your comp doesn't get to engage perfectly, you lose a big chunk of damage.
Worse, when the majority of your damage is from one source, even the enemy squishies can just build (in this case) a MR item or two and be much tankier than yours will be. Not only is Cait your only source of physical damage, but the nature of your engage is to push the enemy away from you and chase them down. Cait's starting off in the backline, which means that she has to continually run up to continue the fight, which means that she won't be doing much (since you can't lock anyone down) and might even get jumped by an assassin.
Basically, without mass hard CC, this is how most of your engages will go: Karthus and Fiddles jump in as Hec ults in. The enemy tank and support CC them and someone pops a speed boost/Randuin's active to peel for anyone who doesn't have an escape of their own. Fiddles ult burns out trying to chase, Karthus doesn't get much damage and doesn't die. Cait is still chasing your team, Kat is waiting for one to get low enough for her to reset. Enemy team turns and locks down one of the people in the front, then collapses on your team. It's the same deal as a Kennen ult except Fiddles and Karthus aren't speedy enough to keep up with people on their own. Sure, there are some comps this will work against, but there are plenty that can shut it down.