Why is it important to use a local system? What is wrong with using the best system for the job wherever in the world it comes from?
If it was a traditional software system that actually ran on the servers owned by the government then that would be fine.
With GA, at the very least Google get to know when I visit the site, and likely which pages I visit, simply through the requests my browser makes.
I'm not familiar enough with GA to be able to judge how much else is transmitted to them.
I guess I'm just very suspicious when personal data crosses borders.
EDIT - also wondering what you mean by a separate deal? If the data goes to the US it goes to the US and is then subject to US laws (and no longer subject to EU/UK protections, deal or no.