In a criminal case, the court-supplied translators needed would be paid for by the loser of the trial.
In a civil case, the language will be specified by the original language of the contract between the two parties in dispute – if not by specific clause, then by the language the contract is written in. The government will not enforce contracts is has not specifically agreed to enforce, so it will probably have rules about what language(s) contracts may be written in, depending on what languages are available in its enforcement courts.
In both kinds of cases, there are two potential needs for a translator. One is so that the parties can comprehend the procedings, and the other is to render testimony comprehensible to the decision makers. The simplest case is the contract case: if the contract is written in English, no translation is needed because both parties understand English, and the trial is in English. On the other hand, if the contract is in Somali or Hmong, then the governmental courts should, as a matter of policy, decline to handle any such contract (to the best of my knowledge, that is the case in the US). In short, governments in the US should never enforce a contract except one written in English. Adjudication must instead be provided by an agreed-upon binding arbitrator, who will be selected because of their competence to adjudicate in that language (enforcement would then be in English, via a bilingual contract where the two versions are stipulated to be equivalent, and the enforcement is of the arbitration contract).
As for the question of translators in a criminal case, there aren’t any linguistic issues of statutory interpretation (unlike a Somali contract case). I’m somewhat sympathetic to assigning the cost of the trial to the guilty party, but I don’t see any reason to distinguish court translations from forensic costs or indeed the cost of paying the salaries of bailiffs, judges, prosecutors, defense attorneys and recorders. The reason for making the prosecution pay the whole cost of the trial is that is would (hopefully) reduce the number of improper prosecutions – only actually guilty people would be prosecuted, since there is a highly significant cost to false prosecution.
Why did I bring up the distinction “participant comprehending the trial” vs. “adjudicator comprehending the evidence”? Because it is mandatory under any legal system that the adjudicator fully comprehend the evidence, so it is essential that testimony given in Somali be translated – accurately – into English, so that the judge and jury can understand what the witness is saying. It is polite but not as important that the defendant have testimony given in English translated into Somali, f they only speak Somali. But all that is required is that his attorney be able to communicate the nature of any important testimony given at the trial to him. Thus the only obligatory translation is non-English into English, not Somali or Danish, and only for the sake of the court.