Trump did not bring Fauci in. He was already in charge of his domain. Has been for decades.
Correct. Fauci has (unfortunately enough) been Director of the National Institute of Allergy and Infectious Disease (i.e., one of the 27 institutes under the umbrella of the NIH) for decades. He is a career civil servant. He cannot be "fired" in the conventional sense, other than "for cause." On the other hand, as a career SES, he is not entitled to remain in his position as Director of NIAID if the head of the Executive Branch -- which, of course, the President of the United States -- removes him from that position. Trump could, and should, have done that immediately.
Meanwhile, what?, do you imagine that, as Director of NIAID, Fauci was somehow authorized to just wander into those White House briefings and press conferences on his own say-so? The Trump administration put him there. This is on Trump, period.
Trump's poor handling of the pandemic from the beginning is why we remain in this mess. Did Trump get bad advice? Sure. Did he also get good advice? Sure. Which advice did he ultimately take? Where does the proverbial "buck" stop, hmm?
But Trump did allow Fauci to have the profile he enjoys to this day. The President could have chosen anyone he liked to be the spokesman for the crisis who would deliver 100% of the government’s statements on the subject. You see this all the time at the state and local level where governors and mayors do not allow anyone else in their administrations to speak on behalf of their government with respect to storms, etc (Think Rudy after 9/11 or Killer Cuomo for Covid).