I have to disagree with you. While assuming Gaussian disturbance terms results in a linear regression, the linear regression framework is more general. It makes no assumptions about the distribution of the disturbance terms. Instead, it merely restricts the variance to be constant over all values of the response variable.
As above, I would strongly agree with you. Both linear and logistic regression can be special cases of frameworks that are more general and far less parametric than GLM. But they also have very intuitive or hands-on explanations, especially logistic regression, which GLM doesn't have.
