Herod wasn't a 'proper' Jew; he was an Idumean, roughly from what's now the Gaza Strip. They'd been forcibly converted a couple of generations earlier, and weren't really accepted. He didn't have much respect for Torah, causing major offence, for instance, but putting an image of a golden
eagle over the Temple gate.
His position was pretty much that of the Hellenising Jews of the previous century, who must
still have been about, though they
had been out of power under the
Hasmoneans, and I don't know quite what
had happened to them after the Maccabean Revolt, which was a major defeat for them. After
his death, there were revolts across
his Jewish territories, suggesting a certain eagerness for change! It's only with Herod
Agrippa I the third generation of the family, that we get a ruler who was actually acceptable to strict Jews.
The big problem I see with the idea of a
mint in Jerusalem is that it was a turbulent city, subject to regular large-scale rioting, the Jews
had a
history of revolts, and I'd have thought that the
Romans would have seen it as too much of a hostage to fortune. The Jews
had never minted silver, and may well never
had permission to do so, though they'd also have needed cooperation from outside to import it. A
Roman client
king like Herod
had very limited autonomy, and certainly couldn't just set up a
mint to suit himself.