As a Unix and Windows administrator who does a lot of Unix scripting and almost no Windows scripting, I'd say that it is in part due to the incredible awkwardness of Windows scripting utilities and APIs, and the difficulty (maybe non-obviousness would be a better word) of running things remotely on a Windows machine.
I mean, WTF is this?
Set objWMIService = GetObject("winmgmts:" _
& "{impersonationLevel=impersonate}!\\" & strComputer & "\root\cimv2")
Part of the problem, I think, is that there is an API. Under Unix, admins are largely scripting the automation of command-line utilities they already use. Under Windows, you have to use this API that is unfamiliar on every level. For example, what does "impersonate" mean? This is a trivial concept to a Unix admin, who is likely to use sudo and su and be familiar with setuid scripts already. But a Windows admin is unlikely to be familiar with any of that; they might know about "runas" (or the equivalent GUI option), but they are far more likely to log in as an administrator when they need to do something admin-y.
And the documentation on scripting in Windows is miserable. For one thing, it's far more "interpreted language" than script, again because they are using an (unfamiliar) API and not commands that they're already familiar with. But I don't think I've ever found anything useful in Microsoft's documentation that wasn't led into by finding someone who was already doing something close to what I wanted that pointed me in the right direction. Nowhere does there seem to be a list of things-you-can-do. It's like you already have to be familiar with Windows internals in order to do the most basic things.
Not that Unix scripts don't often look like line noise. But a Unix admin can start with a script that does nothing but run simple commands that he already knows. ("I always have to run these three commands in succession. If I just put them in a file together, I can do it in one command!") And then he can later progress as he gets comfortable with the situation. In contrast, there's no way for an admin to script "log into server as administrator; click on Start → Settings → Control Panel; double-click System; click on the Computer Name tab; etc." Yeah, whatever he was trying to get to is probably presented through an API somewhere, but there's no way for him to incrementally find that.
So, to answer the question "how can we get Windows admins to do more scripting?", the answer is, make scripting less alien. How to do that, I don't know.
Honestly, the answer is in Microsoft's hands. There's no reason that they can't have a command line utility to do everything that's done via GUI. (There are actually a lot of them out there now, but they're not advertised, they're poorly documented, and they're inconsistent.) There's also no reason that there couldn't be some hint in the GUI as to what that button actually does. Have a tooltip that shows the API object that's being modified. Or document it in the Help window.
There's no problem in shielding users from the internals, but Windows seems to go out of its way to actively hide those internals, even from those who want to find them.