One day after James Mattis announced his resignation as secretary of defense in a scathing letter on the heels of President Donald Trump's sudden decision to withdraw all US troops from Syria, the hashtag #TrumpResign was trending on Twitter in Washington.

But if one safe prediction can be made in a week that was unusually turbulent even by Trump era standards, then it is that any kind of musings about this president resigning are wishful thinking.

"I don't see any chance for Trump resigning, unless there were some impeachment proceedings, the way Richard Nixon did when he resigned," said Mark Fitzpatrick, the executive director of the Washington office of the International Institute for Strategic Studies (IISS). "Resigning would be an admission of defeat for a man who insists on winning, winning, winning, so I don't think we can expect a Trump resignation as a solution to the growing concerns people have."

Read more: Jim Mattis' exit leaves Donald Trump surrounded by yes-men

Mattis' announced exit also dashed whatever remained of the previous hopes about a so-called internal opposition to Trump inside the administration. While Mattis himself had repeatedly tried to slow-walk what he viewed as some of the president's most egregious decisions, that tactic only appeared to work for a limited time, and was ultimately doomed when Mattis' influence began waning months ago.

'Adults out, children in'

While there still are likely some administration officials left who will try use bureaucratic inertia to stymie what they view as ill-advised moves by the president, at the end of the day, they will have to fall in line, said Fitzpatrick. "Trump is the commander-in-chief and people will salute."             

Nevertheless, a commander-in-chief who is increasingly prone to sideline his advisers in making crucial decisions such as the Syria troop pullout and the expected partial withdrawal from Afghanistan — first without consulting people like Mattis and then ignoring their after-the-fact objections — is raising concerns in Washington.

Mattis is widely considered the so-called last adult in the room to be leaving the administration. One-time members of the club such as National Security Advisor H.R. McMaster and Secretary of State Rex Tillerson are long gone; another, White House chief of staff John Kelly, is on his way out.

Read more: Donald Trump's motives for Syria withdrawal remain as murky as its implementation

After a couple of years in office, presidents often find that they have got a rhythm, a sense of what they want to do and what kinds of people they want around them and make changes, said Norman Ornstein, an American politics scholar at the conservative American Enterprise Institute. "But all the changes Trump has made are to get rid of the grown-ups in the room and bring in the children."

Instead of listening to advice from his own experts, Trump appears to be increasingly listening to his gut. Just last month, he told The Washington Post in an interview that "my gut tells me more sometimes than anybody else's brain can ever tell me."

Relying on Trump's gut is worrying

It is precisely Trump's penchant for listening to his gut when making key decision that has scholars worried. "Frankly, that gigantic gut does not have a lot of intelligence, depth or sensitivity to the larger consequences of actions," said Ornstein. "So it's time to be afraid."

The Trump administration and the world, noted the experts, have been fortunate until now that this president has not yet had to deal with the kind of national security crisis that a US president usually has to face in his tenure. 

But eventually, they said, such a crisis, the famous "3 a.m. phone call" to the White House, is likely to come. And with someone like Pentagon chief Mattis, who was widely viewed as a responsible international security leader, gone, the prospects of influencing or intervening in Trump's decision making process have dimmed.         

"Whoever will be secretary of defense will be concerned not to see a world war launched," said IISS head Fitzpatrick, who is also a nuclear security specialist. "Although Trump has an individual ability to start a war and to launch nuclear weapons, there are other people involved who will try to steer him in the right direction should he go crazy."

Read more: Is Trump handing over Afghanistan to Pakistan?

Asked who in the Trump administration could still curb the president's worst impulses, Fitzpatrick, to his own astonishment, mentioned National Security Advisor John Bolton. "I didn't think I would ever be in the position of pinning my hopes on John Bolton being the restraining influence," he said chuckling.

But, he added, "John Bolton is very influential — and whatever one may think about Bolton's neocon tendencies and inclinations to use military force rather than diplomatic solutions — he is not a wild man, he is not a crazy person," said Fitzpatrick. "I hope he will continue to exercise some restraining power over Trump."