Nice to know. Thanks! Maybe I should say only for one-way classification model, there exists a both intuitive (simple) and linear independent parameterization?
One-way model seems unique in some ways. Another example is that its least square means are the same as arithmetic group means for unbalanced design which does not hold for multi-class models. I can find ambiguous wording that may have ignored/forgot this special case (one-way) in web posting, for example, https://online.stat.psu.edu/stat502_fa21/lesson/3/3.5.

"Note also that the least square means are the same as the original arithmetic means that were generated in the Summary procedure in Section 3.3 because all 4 groups have the same sample sizes. With unequal sample sizes or if there is a covariate present, the least square means can differ from the original sample means."