You're arguing semantics really. When I wrote "How challenging do you want that lock? Is it a DC 15, 18, 20, 25, or 30?" for example, you (or I) are deciding that on exactly the criteria for which you consider is making you unbiased and impartial. You HAVE to care because you as DM decide by making that judgment call, believing it is a fair value, etc., etc. By making that judgment call, you are deciding what you want to be considered fair. Honestly, you could just as easily have a "Lock DC rule" where any lock the party encounters will have a DC of 5 + 3d10, giving an average of about 20.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.)
In your vampire's castle example, the lock, even as a good one, might be DC 20 to 25, or even higher. And this is where every DM will possibly differ. Given the parameters of the game world, another DM might think 20 is a good DC. Maybe it is rusted, so the DC is higher or the DM imposes disadvantage? Maybe he drops a clue about that fact, encouraging the players to think, "Hey, we should try oiling it more" or something. By examining the world and making those calls, you are getting what you want, which primarily IMO should be a challenging and fun game for the players.
Do I personally care whether they succeed or fail? Sure! Of course I do, and any good DM IMO would. There are times when I make things harder and more challenging to set them up to think about the situation or maybe even have to try again later on when they have discovered something new. There are times when I realized I made things too hard and what I thought should be a fair fight turned out horribly! I meant to be fair, but made a mistake. Do I let everything go anyway, even resulting in a possible TPK, just because I had everything "set" in the world and that is they way it is now when the encounter happens? No. And I hope you wouldn't either. I will not kill a party when I am DMing simply because I made a bad judgment call. Now, if I set an encounter appropriate to the world/setting that they obviously should shy away from and they soldier on anyway... well, sometimes bad decisions on the players' part will lead to their downfall and I will run out the encounter as it is to whatever end awaits them.
So do I want an encounter to be challenging? Sure. Why? Because it sets things up for the story. If the party plays it in a way I didn't foresee and it becomes easy... well, kudos to the players for doing something clever. Will I be upset? Not at all. Sometimes I want an easy encounter or moderate encounter for other reasons. DMs always want things because they have to create the adventures after all.
Any DM who feels the same is not impartial. I want the players to succeed because then it is fun, but not at the expense of making it too simply and unrewarding. So I make decisions about the game world to make it reasonable, believable, challenging, and most of all fun for the players.
Ultimately, it really does come down to what you want as a DM. If the players need an expert blacksmith, how good does he/she have to be? Where are they likely to find him/her? What IS reasonable in your world? It's, well, whatever you want that makes the game enjoyable for you and your players.
(Sorry if this rambles on too much, it is late at night and I really should probably have just replied in the morning! LOL )