But it also goes back to who is overcoming the obstacle; the PC or the player? Some obstacles will be player challenges by their nature, I simply think some things should be PC challenges.
The more I think about this, the more I convinced there is no such thing as "challenging the character". You can challenge the player's ability to build a character, and you can challenge the player's ability to use what's on his/her character sheet, but you can't actually challenge the character.
I do acknowledge that there's one interesting thing that might fall under the category of challenging the character: I like the idea of players being encouraged to find creative solutions to problems using the strengths of their characters. But pretty much all of the examples offered by the "challenge the character" crowd don't involve creative solutions; it's all been "using a skill" to overcome challenges in pre-determined ways. Persuade the troll king. Pick the lock. Detect a lie. This is attested to by the insistence that one can simply announce "I'll roll [Skill]". As in, "The door is locked." "I'll roll Thieves' Tools."
What we don't hear is:
"The door is locked."
"I'll roll Animal Handling."
Why?
Maybe the guy has double proficiency in Animal Handling and he has a plan involving the tame weasel they found, the chimney, and the set of keys they can see through a crack in the door. (I'm winging this; bear with me.) I still don't see this as actually "challenging" the character, but it is challenging the player to use the unique assets of his character to solve problems.
On the other hand, I don't see who or what is being "challenged" by expecting the rogue to announce, "I'll roll Thieves' Tools". I mean, how obvious and un-challenging is that? You don't even need players: I could write software that could play
that RPG in about 5 minutes.
Ok, back the weasel tamer: if he is going to actually implement his plan, he is going to have to offer a lot more than just "I roll Animal Handling." He is going to have to describe it to the DM, and then give the DM a pleading puppy-dog-eyes look, hoping the DM will say, "Ok, I'll need an animal handling check."
In other words, goal-and-approach. Followed by...because the outcome is uncertain...a DM call for a dice roll.
And just think of all the fun ways this could go horribly wrong on a failed check.
So maybe one reason I don't like "I use Skill X" is because if that pronouncement is enough for everybody at the table to know what you're doing, what you're doing isn't very interesting.