From what I've heard, we've run into the (semi-literal) bottleneck of infants having heads that just barely, or that don't, fit through a birth canal.

This actually happened to my wife. Our daughters head was too big to fit through the birth canal and when she came out (c-section) her head was in the 90th percentile for size.

Looks like we can circumvent that bottleneck with modern medicine but then we run the risk of introducing new problems (faulty immune systems and risk to the mother for example)

If infants can develop brain mass in the womb, why can't they once born?

Brain actually does develop until you're adult, but bones need to calcify and that limits how much it can grow

We need to widen the vagina

Grow babies in large jars, remove all cranial size limits.

> We evolved to have big brains

Neanderthals had the bigger brain, (1600 cm³ vs 1300 cm³ according to wikipedia) and we still extincted them so it doesn't appear to be an ultimate evolutionary advantage.

Well not completely we didn't. Many of us still carry Neanderthal DNA.

But not the genes coding for big brain, so these were not resulting in a significant advantage in the vehicle to ensure their own longevity.

Yes, large brains are obviously very important.

The article says the maximum difference is 100 cm³ while the largest brains are about 1500 cm³, so on average 7% larger means 2% smarter.

But I think a couple of things come into play - one is that our genes might be optimised for a certain size and it's not simple to scale, but requires reprogramming. At least in some species, larger brains just means larger neurons, not more of them.