Regardless of how these large scale coordinated dynamics arose, initially functional and selected for, or just epiphenomena (coupled oscillators?), it seems that they HAVE to have become functional (presumably longer range inter-region communication and sequencing) since timing does matter.

If we assume that brain waves do have (have to have) some effect, then it seems most likely that the effect is either beneficial or detrimental compared to the alternative of uncorrelated brain activity, and therefore is being selected for or against, and as the production of millions of years of evolution, it seems the logical conclusion is that there is some functional benefit to it. The alternative is that the functional effect is merely benign, neither beneficial or detrimental, but this intuitively seems less likely.