The Sixth Amendment right to counsel of in a criminal case (but not always at the expense of the government) is often seen as a sacred right and regarded by judges as something to never refuse. However, there are limits. For example, a criminal defendant cannot demand a change of counsel solely for purposes of delaying trial or for some other ulterior purpose. To read a short summary of a case wherein a judge refused the right to new counsel, click on the following link.
https://www.greghillassociates.com/can-a-criminal-defendant-request-new-counsel-anytime.html.