Possibility of increasing brain speed
There are just too many ways to answer this question. But I suspect all of them will be proxies to the ultimate answer - the goldilocks principle.

To give an example, for the human brain to be faster, it would either have to be smaller, or would consume more energy. There is an optimal balance between the size of the brain and its energy ratio (to the rest of the body). Like many factors, these were heavily shaped by evolution (which in turn is heavily affected by our environment).

You can also argue that a faster brain will accumulate processing residues faster, thus we'll have to sleep more frequently, which may have adverse effect on survival chances. I know it sounds far-fetched, but you can actually argue that the size of the brain is correlated to the distance of earth from the sun. That's the goldilocks principle for you. 

Would strongly recommend:

What is so special about the human brain? (TED Talk)

And the first chapter in:

Gibb, B., 2012. The Rough Guide to the Brain, 2 edition. ed. Rough Guides, London.