Why do enchanters scale so well, if their strongest late game tools are their non-enchanting ones?

When I watch the highest level play like T1 vs GenG in the LCK, I sometimes imagine what enchanters would look like in these games. They are extremely explosive with lots of chain CC and coordinated target priority. Here's some examples.

What's the best contribution that Keria's 6 item Nami (more like everyone else is 6 items) could bring to the teamfight against GenG? The answer is the CC from her bubble or ult. The slow from her E could be ok. But there's no way that healing someone for 700, even with a full heal/shield scaling build, would realistically change a late game LCK fight. That's not what determines fights at this level.

Now you might say that well Nami isn't known to be a scaler. Ok, let's look at Janna. What game-changing impact could Duro's Janna have against T1? Displacing the enemy with Q or ult. To a lesser degree, slowing with W or speeding everyone with passive. Again, the ability least likely to actually win the game is the heal/shield, Janna's E. The enemy ADC is critting for 1k at this point with 2.0+ attack speed.

Repeat for every other enchanter. It doesn't matter if they're a super scaler, it doesn't matter if it's a thematically good game for them or not (Janna countering engage vs stuck against range). The question is, what are their strongest tools in these elite games? Remember, late game, not a 1 item spike with Moonstone.

I've come to the conclusion that their best contribution is almost always CC. I think some super heals or shields can be great, like Milio ult or Seraphine W (big spell on a very long cooldown). Basically the big AoE ones. But the average spammable heal or shield simply isn't having an impact.

My tier list would be something like hard CC > slows/speed ups > shields > heals. I acknowledge that MS boosts do fall under enchanting, although not the purest type, which is heals/shields imo. So if the best late game utility is both hard and soft CC, aren't the champs with an abundance of those, basically the engage supports? And enchanting gets statchecked by 6 item carries DPSing. But that would contradict all common wisdom about enchanters outscaling melee supports.

Where am I going wrong with this logic?