I think you're confusing the Gaussian "process" used in Bayesian optimization with a standard Gaussian distribution. They are very different things - as are Gaussian copulas and what is referred to as the 'Gaussian kernel' (which is not actually a distribution at all) in the SVM. The Gaussian process is a distribution over functions, the properties of which are governed by the covariance function - so the prior over the function, or the assumption about its complexity and form, is determined by the choice of covariance function. Of course it is very important to choose a prior that corresponds to the functional form you are interested in, which is actually discussed and empirically validated in the literature referred to in that post. It's a bit ironic that you are claiming to point out the dangers of making lazy assumptions by doing exactly that.