Why assume independent errors and not independent observations when fitting a linear model? When we fit a general linear model, we assume that the errors are independent. But why not just assume that the observations are independent? Isn't it equivalent, and (in my view) more intuitive?

The observations are assumed to be dependent!
Assume some regression like $\hat y=2x$.
Then we know to expect $\hat y(0)<\hat y(1)$.
However, even if we know that $\beta=2$, we have no dependence between the errors on observations with $x=0$ and $x=1$.
