The DM makes such decisions all the time and is always interjecting bias. How challenging do you want that lock? Is it a DC 15, 18, 20, 25, or 30? Sure, once you make that decision the DC is there for you, but you as DM are still making it.
For the sake of brevity, I'm just quoting this part of your post, because it allows me to address the entire topic more succinctly. It applies in equal measure to placing NPCs within the world.
One of the goals of the DM is to remain impartial in their adjudication. You're not supposed to care, whether or not they pick the lock. If you wanted them to pick the lock, then you have the power to make them succeed, by setting the DC to 1. If you wanted them to fail, then you have the power to make them fail, by setting the DC to 40. The DM literally has unlimited power within the game world, which is why it's important that they don't
want anything; and if they can't help themselves from wanting something, then they'd better have the integrity to not abuse their power by simply making it happen. After all, this is a game about the players and their decisions, and those decisions would be meaningless if the DM just went around fulfilling their own preferences.
When the DM determines the DC of a lock, they don't set it based on any personal preferences for whether or not the party succeeds. The determination of the DC is a judgment call, about what the DM honestly believes is a fair value that describes the lock, based on everything they understand about the world and how it works, and their knowledge of how that reality is reflected in the game mechanics.
Think about it. The party infiltrates the vampire's castle, and stumbles across the treasure room. What's the DC on that lock? You could low-ball it, make it DC 12, and the party would probably succeed. Or you could set it at DC 30, even if that's unattainable by anyone in the group, so they would definitely fail. But either way, you're just telling the players that none of their decisions matter, because events will progress exactly as the DM wants them to progress. The
only way that the players have any agency whatsoever is that the DM doesn't do that. A good DM will never take their personal preferences into account when determining a DC. Instead, they will evaluate what they know about the world, and make an honest determination based on their knowledge of how game mechanics reflect that world. The lock is DC 25, because the vampire is wealthy enough and motivated enough to afford the best lock, and our knowledge of how the game mechanics reflect that reality tells us that the best lock is DC 25. (Setting aside, for a moment, that the rules don't even tell us that; the DM is forced to make a judgment call about how good locks can possibly get in this world, which is compounded by the horrible flaws in the Bounded Accuracy system, but that's getting off topic.)