For the record, I'm no fan of ICE/CBP, but it looks like they're just enforcing the law here.
Putting her in a literal prison and in an orange jumpsuit is overkill. Clearly she just screwed up and thought what she was doing was ok, but isn't a threat. Let her go back to the UK and no longer be eligible for ESTA. How is that not sufficient?
The problem with any immigration service in the world is that they are dealing with non-citizens which lack most protections citizenship would have given them — which means that it may take its sweet time before courts actually hear her defense and probably decide as you suggest (along with introducing a 3 or 5 year ban on entering the US).
Second, I disagree with your stance on strict enforcement without discretion, this often lead to unjust outcomes. Laws exist to serve justice, not just to be enforced blindly.
Third, addressing your "ignorance of the law" argument, sure it may not be a defense, but the expectation that everyone fully understands a convoluted legal system is unreasonable.
Overstaying a visa isn't even illegal and extremely difficult to enforce, and working informally is trivial and pretty much impossible to enforce in a country where citizens don't have to carry ID (sometimes even to vote). Anyone 100+ miles into the country on a tourist visa is basically home free, probably even for life and triply so if they speak English and look European.
So what the US does is put the meanest scariest motherfuckers around in CBP/HSI at the border and then say whatever they need to turn the crank, which does little to someone who knows what's happening but great at scaring a naive German woman who doesn't realize border officers are basically playing a confidence game.
The fact that courts are slow is a problem unto itself that should be solved independently.