The main goal of physical repair of the defect in utero is actually to reduce the incidence of hydrocephalus and hindbrain herniation, which are very common in people with Spina Bifida. The existing fetal surgery reduces the incidence of hydrocephalus from about 80% to about 40%. The improvement in leg and bowel/bladder function is actually a secondary benefit.

My understanding is that the hindbrain herniation (aka Chiari Malformation Type II) is the main cause of cognitive trouble in people with SB. But it's worth noting that it's very far from universal in causing that. Most people with SB are basically normal cognitively assuming they get good early intervention (VP shunt, PT, OT, etc.). Some early cognitive development can be slower as a knock on effect of not being able to move around as much as a baby and toddler, and thus less able to explore the environment, etc.

Source: I'm the parent of a toddler with spina bifida. She's completely on track cognitively and with fine motor skills so far. She's way behind with gross motor skills due to her inability to move her legs very much.