C-section can have its own traumas. For months after being born, my (c-section-born) son would startle and cry horribly at anything that made a snick-snick scissors sound, including certain doors/doorknobs, metal chopsticks, etc. And think of it from the evolutionary perspective and the baby-being-born perspective (vs. our external perspective, birthing or watching/helping), and maybe we can posit shock at the transitions that happen with a c-section (inside, cozy and familiar, and then BOOM: Cold! Bright! Lack of pressure! Loud!).
Less traumatic, maybe, but that still seems unpleasant. You go from this nice, calm environment, with basically zero need to do anything for oxygen, nutrients, waste, etc., and are thrust into blinding lights and noises; suddenly you must breath with lungs (after coughing out all the liquid filling them), the temperature is no longer always perfect, you promptly get to experience hunger and have to scream to be fed... Sure, C-section skips "get shoved forcefully through tiny opening" at the start, but you're not skipping that much.
I wouldn't even be sure skipping that part makes it an better, because that sensation might actually distract from all the others, and while it wears of, the others don't in the same way.