There are some errors in your reasoning, though.
Here's one. When people collect datapoints and observe a difference in one case not present in the other, they sometimes fall into the trap of thinking that their dataset is exhaustive - that it captures all the variables that matter.
In other words, it's easy to start with the observation "women tend to be more represented in fields that exhibit qualities of care and less represented in leadership roles" and conclude that the absence of the variable "has leadership" makes up the core difference.
But this is a conceit that you, the observer, made. Your choice of variables to look at influenced your observations of what is different and therefore important.
Here's a counterpoint that contradicts your observed conclusion. Female heads of state and politicians have been increasing in number throughout the last century, and have done remarkably well in those roles. Has the nature and autonomy of executive power changed like medicine (according to you) has? It has not. It is a sign that you have not taken all variables into account.
Here's another error in your reasoning. Why those variables specifically? How do you know those are the variables your subjects are thinking about? When women sign up to be doctors and nurses and not CEOs, are they expressly telling you the shared decision making are the important variables? Or is it because you inferred that those variables are important because you can measure them?
In the interest of correct methodology, here are some other variables that people have suggested to explain the same data: women are conditioned or socialized into early expectations of caregiving roles; women are rewarded for pursuing caregiving roles in a way men aren't; there are more barriers for women than for men, and so on.
Now are these variables the correct answer? We don't know. It is a complex topic, because humans are complex. It is possible biology and perceptions of role play a part, as does socialization and others.
But what we can do is go a little meta and ask the likelihood that a biological variable is a good explanation in the first place. Consider what a good explanation has to do: it has to provide a causal mechanism, and be able to explain how the cause led to the effect you see. The trouble with every single biological explanation that's been proposed in this area is that they don't provide this causal mechanism. What exactly is it that makes women gravitate towards submissive roles? Is it estrogen levels? Hormones? Menstrual cycles? But then people on hormone therapy, people born with extra chromosomes, people with hermaphroditic parts, and so on should all display manifestly different behaviour and choices, which they don't. To explain these differences, you need to invoke more and more factors, until you end up with epicycles all over again.
More generally, the history of biological explanations simply don't fare all that well in comparison to sociological explanations. A reasonable prior is to assume that it may play a small part, but that larger effects are driven by how society treats and works with people.