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.
Linear regression is extra-special because it's a special case of several different frameworks and model classes.
I should have written that it's better (in my opinion) to think of logistic regression in the context of GLMs, at least while you're learning.
Edit: yes logistic regression is a special case of regression with a different loss function. But it's not nearly "as special" as linear regression.