It seems to me that we often go back on the questions of 1) testing contrasts, 2) having confounding variables in the model. I heard Gael saying that scikit-learn's API for linear models was not optimal. Would it be improved to take 1 and 2 into account, I would be glad to simplify the current tests.
That said, I am aware we should not modify a general library such as scikit-learn to address the need of a more specific one (here nilearn). But, if it turns out that the use case involving 1 and 2 is more and more encountered, maybe it would be worth to have a discussion about it to be considered in scikit-learn.