Are there any courtroom TV shows that are litigations instead of an arbitration?

no. the only time you see litigations on tv is when it is a trial which is aired on television but is not an actual regularly programmed show.

i would say that it is probably because it is very difficult to have to pay judges, jury members, attorneys, bailiffs, court recorders, defendants, etc for being on television.

unless it is a news program like a court case that is being aired and covered by news casters, a regular television program has to pay everyone involved for appearing on tv and the amount they get for it is huge.

for instance, reality tv people on shows like american idol, america's got talent, shark tank, naked and afraid,survivor, dancing with the stars, the voice etc. all get upwards of 25,000 per appearance. so it would probably be too cost prohibitive.