This is an interesting idea, but we can at least imagine a test, and I think at least the public perception is that the test works out backwards (but I don't have statistics).

Suppose you compare the sentences received by men who actually have authority to those who don't, for the exact same crime--shoplifting, for instance. Do we see a disparity in that higher-authority men receive increased sentences for the same crime?

The public perception, at least, is the opposite: the lower status you are, the worse your punishment is, on average. I don't know of a study where everything is held fixed save authority, but when you do your best to match all relevant factors, you still find in the United States that black men--who are shown by implicit bias studies to be considered lower authority than white men--receive longer prison sentences (than white men).

So provisionally, I think the hypothesis should be exactly the opposite of what you propose here: that greater authority excuses bad behavior to a modest extent. If you have evidence to the contrary, please share--but it had better be at least as good a test as the racial test.

So, if the authority bias goes the other way, what does explain the (substantial) disparity?

Another reasonable hypothesis is also one you give: a different perception of the ability and willingness to commit crimes, not because women are perceived have less authority but because they are perceived to be less aggressive and have more reluctance to engage in anti-social behavior.

This lines up with the racial sentencing disparities also.

Now, I think the answer would change if the perception was that the crime was committed by a group: in that case, yes, the person in charge generally is considered to have a disproportionate share of the culpability. But I don't think this is a majority of the cases, so I don't think this would explain any sentencing disparity.

(Also, although I think compassion and authority are somewhat inversely related, I think you overstate the correlation. For example, since you brought up Disney, Elsa, despite having lots of authority, was nonetheless a highly sympathetic figure.)

Whether this has anything to do with "patriarchy" or not I think depends on a clear definition of what patriarchy means. All you need for a sentencing disparity of this sort are (1) laws and (2) discretion in sentencing according to those laws that can follow individual notions of propensity to criminality. For "patriarchy" to encompass that, I think you'd need a very broad definition.

Now, there is another hypothesis that you didn't raise which is solidly patriarchal: women receive shorter sentences because they are the "fairer" sex. The patriarchy seeks, among other things, to shelter and take care of women (as non-equals they are lesser but also more precious, much like, but to a lesser extent than, children), so a patriarchal perspective would lead to a more compassionate sentencing.

I do not presently have any good ideas about how to distinguish the patriarchal-caretaking hypothesis from the expectation-of-danger hypothesis (or how to measure the degree to which each factor plays a role).