Browsers don't share cached assets between different origin domains any more. So the browser cache would only come in to play when you're browsing between pages on the same government website.
But I'm not sure that downloading 32kb on each page load is their biggest problem. It sounds like a lot of the cost of jquery is parsing that javascript on each page load - especially on low specced devices. Javascript parsing traces (as far as I know) aren't reused between page loads at all.
This is an interesting point. Is there no way for cdn-hosted JavaScript to have their JIT results cached? I suppose the dynamic nature of JS might make that pretty difficult. (Lack of hermetic environment around modules, so global variables could change compilation results.)
But I'm not sure that downloading 32kb on each page load is their biggest problem. It sounds like a lot of the cost of jquery is parsing that javascript on each page load - especially on low specced devices. Javascript parsing traces (as far as I know) aren't reused between page loads at all.