It's one thing to talk about the advice in the DMG, it's another to justify a style and say "you're playing wrong because of what it says on page XX of YYY".
I think it's obvious from the text that they're warning DMs to not ask for rolls more than necessary which is good advice. I think it's a leap to go from "[don't ask for a] Charisma check to order a mug of ale" to "never ask for a check because you as DM know there's no chance of success". But it's natural language and open to interpretation.
No, it's pretty clear in what it says. Arguing it's ambiguous is an interesting take. I mean, you have the option to point out that it's one of three ways the DMG presents, and that's pretty good. Or your starting point that it's just advice, do what you want -- that works, too. But arguing that it's ambiguous when the text says don't call for a check if there's no consequence for failure? Hard sell, man. You need to do work to read that as "I want my players to be uncertain and that's a consequence, so I can just use that."
If a player asks to check for traps, they are saying that their PC is actively doing something. That's reflected by a roll of the dice. Telling them that there's no need for a roll is taking away their agency, saying in a sense that no, their PC did not bother to check for traps.
No it's not. Their character does the thing and succeeds. What agency was taken away? You're assuming that, by not asking for a roll, I'm preventing the action from happening? Why assume this? Instead, the character searches, and finds no evidence of traps. They take as much time as is needed. No agency is removed here, unless you're mistaking agency with "get to roll dice just because."
It's similar to if PC casts a fireball at an illusion - I'm not going to tell them that they didn't actually cast the fireball because there's no chance of affecting the illusion. They did decide, based on what they knew, to cast the fireball. They did decide, based on what they saw, to check for traps.
Uhuh, me either. The player has their character check for traps -- this happens. Then, because there's no consequence for failure, they succeed in time to their satisfaction.
I mean, how many times is it necessary to reiterate this? You've spent years arguing this exact point despite how often it's explained that there is no consequence for failure. You imagine that it takes time, and that this is a consequence. I agree -- if taking time is a problem, then there is a check because there is a consequence. However, in many cases, the time taken to check for traps is not relevant to consequence, so that's not a problem. I also don't view uncertainty as a consequence, especially if the uncertainty is actually caused by the check. The check should not be generating fiction by itself, it should resolve fiction. A competent character is going to check for traps competently, so if they can't possibly get a bad outcome, why am I wasting everyone's time pretending that they could. Instead, I assume the character performs competently, or that any mistakes made don't do anything because there's nothing there to do.
Honestly, the approach that says you need to make a check because the players shouldn't know things is because the GM doesn't have confidence that their game can be interesting without manufactured uncertainty -- that generating uncertainty enhances the challenge or immersion of the game. I used to think this, too. But, I've found out that I can provide loads of challenge, and get better buy-in from players if I'm not playing silly games like "you're not sure because you rolled low, even though there's nothing there." Heck, I usually make traps noticed straight off (again, competent characters) and make finding out what the trap is/does/is triggered by the point of interest and execution.
Also, I tend to find the objection that rolling prevents metagaming to be farcical -- an inconclusive result on a roll (whether from a secret roll or a roll in the open seen to be low) that only results in uncertainty is guaranteed to result in metagaming -- either by the player declaring actions to double check something that should have already resolved or by the player choosing to ignore what they know and making a choice they know is probably poor but feeling like they have to do the that because of metagaming (in effect metagaming anyway). It's an unvirtuous circle.