After doing some reading, the reason the US didn't intercept the missiles (and likely why Al-Asad was targeted) is that there were no missile defense batteries there. Apparently, the Patriot systems were moved to other areas to safeguard them (like Saudi Arabian oil facilities) since they were believed to be bigger targets. If it turns out that they'd been moved from the bases in Iraq to guard Saudi oil, there should be hell to pay for Trump.
While the current Iraqi government doesn't have the necessary power to kick the US out, it undermines their legitimacy to outright refuse. It's also wrong. Now the US appears to be (and is) an unwelcome occupying force. If you have no intention of leaving soon, you still participate in the conversation about leaving and start negotiating a time table, which you can then stretch. You don't just say, "We're not leaving."