Nor did the Act give to Congress the authority to appoint or remove executive officials, only the ability to consent to their removal. Appointment and removal power would certainly not have survived a judicial review. Interestingly, when the Taft court overthrew a similar act in Myers v. US, the question of whether such a law could govern Cabinet level officials was left unanswered.
It's also not necessary for a President to run his departments via the Secretaries. Witness for example, the Clinton Justice Department, which was most certainly not controlled by Reno.
From 1867 to 1926 some form of removal consent was in place, and at least three Presidents felt constrained enough by that to complain publicly about it, but the US was hardly reduced to parliamentary democracy status. Johnson's stand against the Act was irrelevent--both for him and for Congress--on both sides it was nothing more than a pretext for confrontation. He survived the struggle, but the Act remained.
As for the question of the US becoming a parliamentary democracy, it would have been a disaster. From its inception, Americans of all political persuasions have been factious and distrusting of government. The Constitution is as much an instrument of disabling government as it is empowering and defining it. Parliamentary democracies allow sweeping changes to be made on the basis of very narrow majorities. The de facto establishment of a parliamentary system would have meant the end of the United States, but in any event, it could not have occurred, because the apportionment and election of Congress would still have remained in the States, not in a proportional national representation. The US would at worst have a very strong legislature, but certainly not a Parliament.
I don't think Johnson's challenge failed.
He removed Stanton, contrary to the act, and Stanton did not get his job back.
Truth is, Johnson was politically finished anyway, because he was not going to cooperate with Reconstruction efforts, and the Republican-dominated Congress was going to drive forward most forcefully.
I would say that the later presidents who complained about the Tenure of Office Act were not in the same position as Johnson: they were not at war with the Congress in the same poisonous environment. They appointed their own cabinets, after all (Johnson inherited his).
The peculiar circumstance under which that Act was passed was indeed to protect the Lincoln Cabinet against a distrusted Southern President, and to provoke him as well.
It succeeded in provoking him, and succeeded in getting him impeached, but not removed from office. It did not prevent him from getting rid of Stanton, the kingpin in the Cabinet. That's why I would say that, on the issue, Johnson succeeded. He defied the act, removed a hated rival, and kept his office.
It is interesting to me that other Presidents, thus far, have not attempted this sort of brinksmanship again. It's the Gavin Newsome gambit: acknowledge that the law says what it says, but call the law unconstitutional and break it using executive power, then daring someone to do something about it. With Gavin Newsome, of course, there were many officials above him. But imagine a President Clinton doing it, secure in her knowledge that the Democratic minority in both houses was big enough to absolutely prevent her removal from office in an impeachment.
Now imagine that she added to that the Jacksonian and Lincolnian precedents of outright defying Supreme Court decisions.
So long as 34 Democrats in the Senate held firm, she could not be removed no matter what. This would turn us into a Presidential Republic.
Well, unless the miltary and national security officials who took their own oaths to the Constitution under advisement and acted unilaterally, which could end up in a Praetorian Republic.
Politics could not degrade from there much, because once the veneer of legalism and voluntary obedience to law by high officials is breached, Praetorian Republics have the virtue of being able to enforce their rules on their officials...