...most Protestants consider churches with bishops to be simply Catholic churches under another name.
Who are "most"? The largest of the schismatics are the Orthodox, then probably the Lutherans and the various Anglican derivatives, iirc. All of them have what they call "Bishops". Who is left of consequence?
I did say Protestants, right? The Orthodox are hardly Protestants ~ at least not considered by the RCC, nor any others. The next largest body of Protestants show up in a myriad of names ~ sans bishops. The Anglicans and the Lutherans are probably a fraction off that, and with some of them clearly no longer even pretending to be Christians, we could discuss them on that score all day long, and then there are the Holy Rollers ~ exceedingly popular as an option to RCC in Latin America.
Some groups, the Methodists for example, have someone they call a bishop. His job is fund raising and ministerial retirement programs ~