That was Mike Pence who brought Fauci into the task force. You can blame him but it was the Senate Republicans who wanted to make Fauci the face of the task force. Trump brought on Atlas in the summer and stopped having Fauci show up to the briefings, but by then it was too late.
Trump was President. Trump was head of the Executive Branch, and bringing in Fauci was an Executive Branch function. The buck stopped with Trump.