It used to happen much more often back before conventions were essentially reduced to a candidate live action commercial.
The real reason today is that to run as an alternative candidate in one's own party would be a fruitless exercise.
Unless you're a billionaire (think Ross Perot) you just wouldn't have the access to the money to compete, and the party would try and chop you off at the knees to avoid a potential vote split.
You'd not get the Super-Pac money, wouldn't be allowed in the debates and even ballot access would be a chore.
Back when Abraham Lincoln ran for president, the government footed the bill for the travel of candidates
and the arrangements of having the candidates on the ballots.
However, since then the 1% most wealthy, otherwise known as Robber Barrons at the end of the 19th century
worked to remove government funding for candidates and elections so that corruption would become
entrenched in American politics and to ensure that only the most wealthy would be represented.
But back to the current problems of the current president dismantling health care and welfare services
and then holding those services and everything else hostage each month with a monthly government budget.
Although some would like to argue that a border wall would make America more secure.
Shutting down government so that the armed services are not paid and cannot
effectively defend America from foreign threats, is the opposite of security.
We cannot tolerate the president shutting down government or otherwise making an end run around
the democratic process to try to force a border wall on the American people who clearly do not want it.
There are some options though, such as holding a special election for a new president to replace Trump.
Since we clearly can't have the current president running off to a vacation resort every weekend
while our nation falls to pieces from negligent neglect of duty.
Allowing the current president to hold our entire nation hostage for a monument to his ego
(the border wall) is clearly an unacceptable situation requiring impeachment.