So if instead, the government asked for Apple's source code, build system, code-signing key, and flashing hardware, would that be okay to you?
It's not completely unprecedented to require active assistance from a third-party. There's a Supreme Court case about this very issue, United States vs New York Telephone Co. The FBI wanted New York Telephone to install monitoring hardware on their premises and assist the government in its operation. The district court issued an order to that effect. The company offered to instead give the FBI only information, which the FBI could then use to install and maintain the system themselves. The Supreme Court ultimately ruled in favor of the FBI.
The main criteria that people have read out of that case is "unreasonable burden". I don't think that the FBI's request to Apple is an "unreasonable burden", especially since the government will pay for any costs. The biggest burden will be on Apple's reputation, but that is self-inflicted from making claims (honestly or not) that ultimately weren't true. I can't imagine the court allowing Apple to keep its technical assistance from the government.