That'd be the end of any chance of suing the government. A large number of Trump's proposed policies (eg. the Muslim ban) would've passed through without resistance because no lawyer is going to sue the organization that signs their paychecks.
We already have the concept of separation of powers. Judges are paid by the government, but issue injunctions agains and rule against the government all the time. We make sure that this is under the purview of the judiciary.
