The existence of a chief executive officer of the state introduces a conceptual problem: how can you enforce the law against the person who has the final say on law enforcement? It is not possible for this enforcement to come from within the executive itself, because that would introduce an infinite regress problem — the only person who could enforce the law against the president would be a meta-president, and who could take action against the meta-president who failed to enforce the law properly, etc., etc.? The legislative and judicial branches technically “check” the behavior of the executive, but the Bush era shows how easy it is for a motivated executive to elude both constraints: by issuing “signing statements” declaring the intention to construe laws in counterintuitive ways, for instance, or by either ignoring court orders or carrying out illegal activities in places where the courts do not have jurisdiction. Both restraints are fatally weakened by the necessity that it is precisely the executive branch that must carry out the law and the legal judgments — putting us right back where we started.
The congressional power of impeachment is the only effective check on presidential action, but it presents an almost impossibly high bar to removal. Only in the most extreme circumstances will there be a 2/3 majority of the Senate willing to actually remove a president, even leaving aside partisan loyalties. The fact that no president has ever been impeached and removed from office should show that the impeachment power is all but a dead letter. (Nixon is not a good counterexample — he left office on his own terms and was pardoned by his successor, avoiding all legal consequences for his crimes.)
The only answer is not to have a president in the first place. An executive with its own independent popular mandate is a disaster waiting to happen, especially when the path to impeachment is so arduous. Even worse is the fact that there is no provision for a special replacement election, making it virtually impossible to remove an entire administration.
The parliamentary model, where the executive is a creature of the legislature, is the solution to this well-known problem. Any government that does not maintain the confidence of the majority of the legislative can be removed through a simple vote, and elections can generally be called at any time. Unfortunately, it is nearly impossible to imagine the US heading in a more parliamentary direction, due to the huge obstacles to amending the constitution — we can’t even get rid of the Electoral College, for God’s sake! — and so the most likely constitutional evolution will be to continue along our current path toward more and more dictatorial power for the president.
Trump’s foolishness and incompetence might slow that progress, just as Nixon’s betrayal of trust did, but we cannot realistically expect that even the successful removal or resignation of Trump would lead to a full reversal. If anything, his unique personal qualities could further reinforce the legitimacy of the presidential regime as such, as long as a “normal” candidate occupies the office.
An und für sich 
Lest you think I’m only coming to this conclusion because it’s Trump, I quote a letter to the editor I published in the Chicago Tribune during the Blagojevich scandal:
Rod Blagojevich’s apparent attempt to sell Illinois’ vacant Senate seat is appalling, the latest in a long line of unethical and irresponsible behavior. But it is ultimately only a symptom of a much deeper problem: The office of governor is simply too powerful. State constitutions tend to imitate the federal Constitution, but whatever the virtues of a strong executive at the national level, there is simply no reason for a strong executive at the state level.
The office of governor should be reduced to a purely administrative function with no unilateral powers such as pardons or Senate appointments—and should ideally be appointed by the legislature to avoid any pretense of a popular mandate for independent action.
The apparent establishment response to this very real issue is to push dubious ideas like “the principle of FBI independence” — I actually recently saw a New Yorker article which listed this as one of the crucial democratic values. Yes, secret police independence is vital to democracy. That would make J. Edgar Hoover a key architect of our constitutional order.