I am usually not wont to defend the dysfunction presently found in the USA federal (and state-level) judiciary, but I think this comparison to the German courts requires a bit more context. Generally speaking, the USA federal courts and US States adopt the adversarial system, originally following the English practice in both common law and equity. This means the judge takes on a referee role, and a plaintiff and a defendant will make their best, most convincing arguments.

I should clarify that "common law" in this context refers to the criminal matters (akin to public law), and "equity" refers to person-versus-person disputes (akin to private law), such as contracts.

For the adversarial system to work, the plaintiff and defendant need to be sufficiently motivated (and nowadays, well-monied) to put on good arguments, or else they're just wasting the court's time. Hence, there is a requirement (known as "standing") where -- grossly oversimplifying -- the plaintiff must be the person with the most to gain, and the defendant must be the person with the most to lose. They are interested parties who will argue vigorously.

Of course, that's legal fiction, because oftentimes, a defendant might be unable to able to afford excellent legal counsel. Or plaintiffs will half-ass or drag out a lawsuit, so that it's more an annoyance to the opposite party.

In an adversarial system, it is each party's responsibility to obtain subject-matter experts and their opinions to present to the court. The judge is just there to listen and evaluate the evidence -- exception: criminal trials leave the evaluation of evidence to the jury.

Why is the USA like this? For the USA federal courts, it's because it's part of our constitution, in the Case or Controversy Clause. One of the key driving forces for drafters of the USA Constitution was to restrict the powers of government officials and bureaucrats, after seeing the abuses committed during the Colonial Era. The Clause above is meant to constrain the unelected judiciary -- which otherwise has awe-inducing powers such as jailing people, undoing legislation, and assigning wardship or custody of children -- from doing anything unless some controversy actually needed addressing.

With all that history in mind, if the judiciary kept their own in-house subject-matter experts, then that could be viewed as more unelected officials trying to tip the scale in matters of science, medicine, computer science, or any other field. Suddenly, landing a position as the judiciary's go-to expert could have broad reaching impacts, despite no one in the federal judiciary being elected.

In a sense, because of the fear of officials potentially running amok, the USA essentially "privatizes" subject matter experts, to be paid by the plaintiff or defendant, rather than employed by the judiciary. The adversarial system is thus an intentional value judgement, rather than "whoopsie" type of thing that we walked into.

Small note: the federal executive (the US President and all the agencies) do keep subject matter experts, for the limited purpose of implementing regulations (aka secondary legislation). But at least they all report indirectly to the US President, who is term-limited and only stays 4 years at a time.

This system isn't perfect, but it's also not totally insane.