In US Federal court, rival lawyers don't make requests to the judge, they make requests of each other. The judge is merely a referee, who adjudicates disputes that arise as part of the process. Example:
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.