Would we be smarter if our brains were more interconnected?

I know that the different parts of out brain do talk to each other, but only to a certain extent. We’ve still got separate, compartmental information and processing.

Here is the link to a 20/20 show, “7 Wonders (part 4)—Daniel Tammet”, if you’re not familiar with him.
He has an incredible mind, and I don’t want to take away from it in any way. I know it’s much more complex than one concept.
But, it was one concept that caught my attention: synaesthesia, at the 3:00 mark. It’s a very brief explanation, but it got me wondering a bit.

Synaesthesia is a condition where the different brain regions do talk to each other, where they cross over quite a bit.
Tammet’s explanation of how he thinks about math, I can’t even fathom. It’s not numbers he sees, but images.
I’m not saying I think everyone should think exactly like him. It’s just, this one ability of his, of his brain, to be able to communicate more fully with itself—this isolated function—it seems to only help him.

And it got me wondering, why most brains don’t work that way, too. Wouldn’t any increased amount of communication only help our minds? Rather than having everything so seperate and cut apart, having a wonderful mesh of everything as it collides together, colorful and vivid. It seems like the compartmentalizing is only putting up walls and barricades.

It’s the way our society(ies) more or less approach life, too. Dividing things, sorting things. We teach specified, separated subjects in school. We work in specialized, specific jobs. We’ve got art fields and science fields. Numbers, letters, pictures. All, for the most part, very distinct in their differences.

I’m straying…

My question:
Why are our brains so divided and separated?
Can we work to make them more connected?
Wouldn’t combining our personal capabilities, rather than isolating them, only make us smarter and more able? Like people can create more when we work together, our minds could create more when its parts work together?