I am not expert on this subject but am posting to recommend a great article in the Weekly Economic Commentary of Northern Trust (forgive lack of direct link but you can no doubt access it via www.northerntrust.com)

Outline of key points to hopefully tweak your interest in this pretty complex issue:

The push by the Administration to tie the Fed to political policy is not new and the US Fed did not split from the Department of Treasury until 1951.  Though there are arguments for independence and though most advanced economies do have an independent national banking system, it is by no means universal.

The argument to tie the Fed to the Executive is to have the government as a whole aligned with policy set by persons named by the electorate. The argument to keep the Fed separate is that it acts as a check on economic policy, much as courts act as a check on other executive actions.

Large government deficits and inflation historically often align with banking systems tied to the executive.

A politically aligned Fed will control membership in the regional Reserve Banks, could result in parking assets supportive of an Administration’s industrial policy, could alter general approach to inflation, could effect swap lines with other central banks and thus affect ability to respond quickly to crisis situations; could track Project 2025 agenda items (eliminating the Fed’s mandate to maximize employment, consider moving to a gold or commodity-backed (eg currency) standard to back up currency).

Financial market negative reaction might harness the current Administration drive to align the Fed, although this point seems to me to be wholly fact-dependent and presently unclear.

Whether you the reader agree with the Northern Trust position in favor of independence or agrees with the thrust of the current Executive, I recommend this article as putting meat on the bones of what to me had felt just like a simple line drawn between liberal and conservative political camps.