[aquafox]

I agree with your points and thats why it's useful to compare a MLE to an alternative model via a likelihood ratio test, in which case one sees how much better the generative model performs as compared to the wrong model.

Similarly, AIC values do not make a lot of sense on an absolute scale but only relative to each other, as written in [1].

[1] Burnham, K. P., & Anderson, D. R. (2004). Multimodel inference: understanding AIC and BIC in model selection. Sociological methods & research, 33(2), 261-304.