Doesn't the non-Gaussian source assumption of ICA render it practically useless? Gaussian distributions appear everywhere in nature, indeed this was largely the justification for most classical methods' reliance on assumption of normality.
ICA assumes non-Gaussian sources, indeed it requires this assumption to hold for the derivation of components via Central Limit Theorem.
But what then is the value of a method that only works with assumptions contrary to the known reality? Note that unlike the many previous questions I am not asking why or how ICA requires non-Gaussianity. I understand and accept that ICA requires this. What I don't understand is how this doesn't destroy the perceived usefulness of ICA.
What if one wished to separate a mixture of Gaussian sources? What if one didn't know the distributions of the sources (as is typical), then it would seem the 'default assumption' should be for rather than against their Gaussianity - in this case a method that can only give non-Gaussian answers is surely misleading at best?
Are scientists really just 'flip-flopping' on how Gaussian they assume the world to be when they use ICA versus classical methods?
 A: ICA essentially reverses the central limit theorem: if averages (or generally speaking: linear combinations) of data becomes more and more Gaussuan, then one way to uncover the original signals from a linear combination of unknown sources is to look for those that are most non-Gaussian. The more non-Gaussian data you find, the closer to the source you should be.
ICA for all Gaussian signals won't work. Use PCA then, also since co-variance structure is all you need to know anyways about the data if its multivariate Gaussian. 
Re Gaussianity:
An interesting article i can recommend is "Why Gaussianity?" (https://ieeexplore.ieee.org/document/4472249/)
One takeaway is that Gaussianity is the max entropy distribution for given mean and variance. So the reason we often assume it in methodologies/models is because we want to assume a world under most uncertainty possible for any method to (still) work.
Re reality is Gaussian:
While averages become more Gaussian, "reality" is in fact not (!) Gaussian (speech, income, # of people you know, stock market, color distribution in images, word frequency, music, traffic delay times, temperature, neural brain activity, seismic activity, ecg heart signals, ...). So most of the times you see Gaussian in 'reality' it's either averages / combinations of other signals (-> ICA comes in handy) or brownian motion - i doubt you see the latter very often ;).
