Basically you're complaint here is about formality and paperwork. Which, fine. It sucks. But the fact that it exists is precisely what prevents someone from doing stuff like paying off the judge or just destroying evidence. I don't love it either but I sure as shit know which system I'd rather be living under.
[1] It's also actually wrong as a matter of pedantic fact: discovery requests are court filings and are made "to" the court, not the opposing counsel. But again, that's a distinction without meaning.
"Paying off the judge" is not a systems-level problem; it's the sort of thing that has been criminal for as long as man has had legal systems. You can't point to it as an example of "legal system is good" or "legal system is broken." Doesn't work that way.
It literally criminalizes it! People go to jail and lawyers get disbarred for obstruction every year. And as a result reputable firms won't even try to dance around these things. If you're an attorney and get a subpoena or discovery request, you tell your client to freeze their backups right away and send repeated emails reminding them, then print them out and file them along with the response. This is true even if it's a ridiculous request you know you'll beat. Because you know if you fuck this up you'll lose your career.
I mean... have you ever actually talked to a corporate lawyer?
https://www.law.cornell.edu/rules/fre/rule_614
Rule 614. Court’s Calling or Examining a Witness
(a) Calling. The court may call a witness on its own or at a party’s request. Each party is entitled to cross-examine the witness.
(b) Examining. The court may examine a witness regardless of who calls the witness.
(c) Objections. A party may object to the court’s calling or examining a witness either at that time or at the next opportunity when the jury is not present.
Red-Team Lawyer: "Provide us with all emails from 1/1/2010 through 1/1/2020, inclusive, that include or mention [product x] or are of relevance to its research, development, production, or marketing."
Blue-Team Lawyer: "That's overly broad and many of those emails contain proprietary confidential and trade-secret information, which is protected. My client will not provide them."
Judge, intervening after objections are filed: "Counsel, under FRCP 26(b)(1), discovery must be proportional to the needs of the case. Red Team, narrow the timeframe to 2015–2020 and limit the search to emails involving R&D leads and marketing executives. Blue Team, designate confidential portions under FRCP 26(c) as 'Attorneys’ Eyes Only' and produce a privilege log for withheld items. Failure to comply may result in sanctions under FRCP 37."
Every single part of this costs money and takes time. It usually takes a judge ~1-3 months to rule on discovery disputes. Filing the dispute is non-trivial. And "designating confidential portions" can provide junior attorneys with months of work.
That's hardly even the tip of the iceberg. There are so many sneaky tactics you can use in discovery that entire books have been written about them. For instance: https://jamespublishing.com/product/guerrilla-discovery/
Whereas if both sides just provide their evidence to a judge's office which compiles them into an account, all of this cost and effort is spared.