No, federal employees should not be "at will"
One of the things President Trump wants to change is to make federal government employees easier to fire. Clearly reform is needed, to make it easier to remove federal employees who are incompetent, lazy, insubordinate or otherwise poor employees. The most egregious examples are things like federal employees watching porn at work instead of working, and are very difficult to terminate despite this behavior. But here is the problem: Extreme cases make bad law, and making all federal employees "at will" goes too far in the other direction.
Having all federal employees be "at will" in 1917 would have been more feasible, but the federal government is called a leviathan for a reason. Government is simply too big for large-scale changes when a new administration takes office, which is what would happen if all employees served at the pleasure of the President. It would be extremely disruptive, would reduce services to the taxpayers, and would demoralize employees. It would incentivize abuse of power, as well as putting in unqualified employees to replace the qualified employees that are fired on an "at will" basis.
Furthermore, government should have fewer rights than private employers. If a private employer does not like someone's political opinions, that employer is free to remove that worker. The federal government is bound by the First Amendment to not punish employees' political speech. There is more leeway when dealing with employees than the general public, obviously, if an employee is being disruptive to the work environment. (That can be abused, obviously.) But the reason that we have the protections in place for federal employees is to prevent abuses of power. To the extent that the protections allow bad employees to continue to collect a paycheck, they should be reformed.
We have seen locally the kind of chaos that can result when new elected officials clean house when they take office. That would be magnified many times over if federal employees were "at will" the way city and county employees are. Making massive changes in the structure of federal employment in response to the extreme cases of porn-watching employees is not in the best interest of the taxpayers, the other employees or the interest of an efficient government.