Indeed, prosecutors do not think about legal precedent. There is nothing stopping them from trying to win a case illegally. However, a guilty ruling can be appealed by the defendant to another court, which will look at the original case and undo the guilty decision if it was achieved incorrectly. The judge hearing the appeal will interpret the law strictly. Only in situations where the law is vague can precedent be set. Precedent means that in the future, judges considering the same vague law will try to interpret it consistently with past interpretations. If a judge ruled that a blatantly illegal court procedure could stand, then this ruling would also be appealed. Appeals can go up a chain of appeals courts all the way to the Supreme Court.

If a prosecutor blatantly broke the law to win a case, and the judge allowed it or colluded with it, and an appeals review made this known, then this would adversely affect their careers. This, combined with that most prosecutors and judges want to follow the rules, is an effective deterrent against illegally obtained evidence.

Even if a prosecutor thought, similarly to you, that it's worth breaking the law to win a case, they are discouraged from doing so by the appeals system.