Didn't have a chance to get back to this yesterday. Lot's and lots of posts since then veering into metagame territory instead of the topic but here goes ...
I did bypass some of the double checking what others were doing for brevity, I assume whoever is running the rogue is either on their own for some reason or discussed options with the group after the open lock failed.
Sure! I agree, a lock is probably a better example to use, as it has fewer moving parts, so it cuts to the real issue more directly.
I actually think the specific verbiage of how skills are used is very relevant. I think a lot of our misunderstandings are coming from assuming that these sorts of specifics don’t make much difference, when in reality they make all the difference. But, I will try to engage in the example as you present it.
This looks a lot like the way I’ve seen other DMs run such situations, and if you enjoy that, awesome. I’ll try to follow along with the same scenario, but more how it would look if I were DMing. An important thing to keep in mind is that I use periodic checks for complications (which can include wandering monsters, but also other things that make the PCs’ lives more complicated) to apply time pressure. A lot of player decisions come down to managing time. I use different time scales for different contexts, but basically a time-consuming action eats up about a sixth of the interval between checks for complications, and a dangerous action can trigger a check for complications early. Some actions are both time-consuming and dangerous, some are one or the other, some are neither. With that out of the way, here’s how that scene might go at my table:
DM: The door has a padlock on it.
Joe: I take a closer look. Is it trapped?
DM: I am hearing your goal is to find out if it’s trapped, could you be a bit more specific about how you try to find that out?
Joe: I don’t want to touch it or anything, I’m just giving it a thorough visual inspection.
DM: You don’t see anything out of the ordinary for a padlock of this make.
So it's just the description of inspecting? No check? This is something that I dislike, using player skill which tends to end up being "knowing what the DM wants to hear" over PC skill. Someone who is more naturally eloquent or simply knows the DM better will be more likely to succeed. More below.
Joe: Ok. I want to try to pick it.
DM: Alright, it’s going to require DC 20 Dexterity check to open, and I’ll add a die to the time pool.
No clue what a time pool is. Some house rule borrowed from another game? [edit: house rule explained pages ago]
Joe: Hmm… Alright, but I want to spend inspiration to get advantage on the check.
DM: Sounds good. Alice, what are you doing during that time?
[I’d go around the table getting everyone’s action declarations before proceeding to resolution, then…]
DM: Ok, how’d you do on that lock, Joe,
Joe: Only a 17, so I haven’t got it open yet.
I’d then proceed with resolving the other players’ actions, re-establish the scene accounting for what changed as a result of those actions, and ask what the players what they want to do. If Joe wants to keep trying for a half hour, that would be two repetitions of this cycle, but one of the advantages of this method is that he doesn’t have to commit to the full half-hour. After each attempt he can re-assess the situation and decide to keep going or try something else instead. As time advances towards the next complication roll, this may affect the players’ priorities and strategies, just as it would the characters’.
Awesome, I hope it goes well!
We will shortcut stuff because the players trust me to not "gotcha". If inspecting something is potentially dangerous we'll go into details. Vast majority of time it's unnecessary filler to add extra detail that doesn't add anything for us so "I investigate" is good enough. I assume the PC knows how to do their job, the player does not need to know.
The discussion over assuming the PC is the competent one vs player descriptive skill is a divide as old as the game. I remember back in ye olden days having this discussion, that my PC knows how to search the door for traps and what to look for without triggering the trap. I, as a player, do not. So been there, done that, long ago. I just ask for an investigation check and I, or the player, may embellish at times depending on if it's interesting. There could be times when it's more complex than a simple roll. That's fairly rare because traps and whatnot are not generally a focus of my game.
Next is the issue I have with telling the player "it's a DC 20". As I said, that takes me out of the descriptive narrative. It also gives out too much info. Let's say the lock is designed to look like a standard commoner's lock. The equivalent of the basic masterlock you get at the hardware store so it should be easy (DC 15). But the shed is really owned by the local crime lord so it's a higher quality lock disguised to look like a cheap one and it's hard (DC 20). Maybe the investigation check could have detected this, maybe not since the mechanism will not be open to visual inspection.
Point is that sometimes until you try something you don't know. I have no idea how many times I've started something that I thought would be an easy task that was much more difficult once I started. I want the game to reflect that and sometimes it does, hence "it looks easy" becomes "when you attempt ___ it's much more difficult than it looks". That cliff that looks like it has plenty of handholds? Turns out the rock 10 feet up is extremely fragile making the climb more difficult. Or the light was such that you couldn't see the handholds.
People would be frustrated if I told them it looked like a DC 15 but instead it was a 20. In some cases, there's simply not enough information to make an educated guess and I will tell them that they simply can't tell. How do you know how hard it is to dig a hole for a post until you try? I mean if your nephew gave you a couple of "easy set" posts that you just screw into the ground and they put them in easily in 5 minutes and
you try but then there's rocks every 2-4 inches you have to dig out by hand? Something that should have been simple ends up taking close to an hour and then it doesn't really work and you have to go back next year with the quickcrete and ... wait I'm digressing again.
Point is that sometimes you can tell how difficult something is, sometimes you can't, sometimes you make a guess and it's wrong. Absolute certainty before attempting a task is not a given unless it's a simple repetitive task.
In addition, setting the scene is not generally something I would "reset" unless something changes. As I said in my description, I would just let the player tell me what they thought a reasonable time to try was and go with that unless something external changes. My DMing just isn't that formal.
Last, but not least, everything you describe is things I've experience, just not all at the same time. Can you
please stop talking about how I might like it if I tried it and accept that after playing for decades I've experienced most options?