"I think that for (Trump), he believes he needs to project invincibility. He thinks that's the most important thing, that's what people want to see," said David Smith of the United States Studies Centre at the University of Sydney.
"But he's the president of the United States. What people want to see is responsibility, and he is showing no responsibility," Smith told "Street Signs Asia" on Tuesday.
The 74-year-old president was discharged from Walter Reed National Military Medical Center on Monday, after three days at the hospital where he was receiving treatment for Covid-19. Medical experts previously warned that he should remain in hospital given his age and the "stealthy" nature of the virus, but Trump said on Twitter that he was "feeling very good."
The president's doctors said Monday that his condition had "continued to improve" over the last 24 hours, and he will continue to be treated at the White House.
Trump was also criticized for going on a drive outside Walter Reed on Sunday, during which he waved to his supporters gathered outside the hospital. Doctors said he put his Secret Service agents at "absolutely unnecessary risk" by getting into the vehicle while "actively infectious."
More than 35.4 million people have been infected by Covid-19, and at least 1 million have died, according to data compiled by Johns Hopkins University.
Smith said the president seems to be taking "more and more steps" that put the people around him at risk.
"When the United States seems to be on the brink of a third wave of the pandemic, which has already killed more than 200,000 people, I don't think that that irresponsibility is going to be rewarded," he said.
However, Frederick Kempe, president and CEO of the Atlantic Council and a CNBC contributor, said Trump was playing to his base and knows that the only way he can win is by "solidifying" that support ahead of the Nov. 3 election.
"What you saw him just do today is something that goes against all health logic," he told CNBC's "Capital Connection" on Tuesday. "But it plays entirely into the person that his base loves and continues to support."