Why is there such a disparity in CD rates between local banks and national (online) banks?

I have a 12-month CD maturing in about a month, from a local bank here it Atlanta. I have been shopping around for what I might want to do with it.

The local banks here (and even the local branches of the national chains) are offering pitiful interest rates:

Chase .10%
Bank of America .25%
BB&T .35%
Wells Fargo .20%
local credit union .45%
and so on..

When I look at the national (online) scene, I see rates like these:

Ally 1.05%
Synchrony Bank 1.25%
BBVA 1.35%

And there are any number of competitive and insured offerings in that same ballpark.

I suppose I would mildly prefer to have a local person to talk to, but not at the cost of a full percentage rate return. Rates are bad enough as it is?

Why aren’t the local banks competitive? Do they think people are suckers?

Is there a cogent reason NOT to move my CD to one of the national internet banks and earn 2–3 times the return?