Let me try an example. There's a door that has a contact poison on the handle. For whatever reason, the players are suspicious of the door and are checking for traps.
The two methods you're contrasting here are asking for a roll vs stating an approach and goal. Let's start with asking for a roll.
"I search for traps. I got a __."
Firstly, this method requires a fixed DC fir the trap. This is a somewhat arbitrary DC based more on the needed challenge rather than anything hapoening on the fiction. That's not bad or wrong, just hiw it is. Many (most) published adventures set DCs this way.
So, a the check result is compared to the DC. I'm pretty sure we'll all agree what happens on a success -- the poisoned handle is discovered! But, what happens on a failure? That's murky. Some tabkes will offer "you find nothing" and wait for further actions that may engage the trap. Others might deckare that the poison was touched, which sets up the "I didn't say I touched that!" argument. The failure options are either 'nothing' or assuming actions on the PC's behalf that are harmful. And, this is perfectly fine if the table agrees the GM has this authority over PC actions. Not my preference, but perfectly fine.
Now, the goal and approach method. This method modifies DCs based on declared actions, so already a difference, and also generates different outcomes based on deckared actions. It is, however, not pixel bitching except in a very degenerate form. Let's look at two example approaches:
1) "I carefully examine the door visually to see if there are any traps."
With this action, the GM will probably determine the outcome is uncertain. A DC will generate based on what the GM thinks is a good representation of noticing the contact poison by visual inspection. A roll is then called for. On a success, the result is indistinguishable from above -- the trap is discovered! On a failure, though, the range is limited. The result is "you don't notice anything." Touching the poisoned handle is not a possible outcome. This is difference.
2) "I check for traps by carefully and slowly opening it, feeling for catches or triggers."
This plays out a bit differently. The GM could determine this directly engages the trap without a roll and move there. I'd, personally, set the DC as above and call for a roll, but I go with the assumption PCs are competent. A success would notice the poison before grasping the handle, so same as above. A failure, though, does not involve the GM assuming action from the PC -- tge handle has been grasped.
So, then, goal and approach work the same as asking fior a roll in success conditions (usually, there are corner cases), but in failure conditions they usually operate differently -- one establishes failure conditions from the approach declared, the other leaves it up to the GM. Neither is inherently superior.
Now, to address the complaint you make about pixel bitching more directly. Yes, goal and approach in a degenerate form is pretty much pixel bitching. If you, as GM, are looking only for the magic approach phrasing, you're doing the bad. But, as in all things, comparing how you play, with your principles and guidelines robust and intact, to a degenerate form of another's play, you will always look good by comparison.
Goal and approach is used in a principled manner not to create the need for specific approaches, but to reduce the need for GM assumptions. Done in a pricipled manner, goal and approach is very lenient on approaches, as I show above in the example where there's still a roll for an approach that appears to go straight at the trap. The priciples here is "don't be a dick" and "assume PCs are competent." I use goal and approach because I want to give the player the authority to say what their PC does -- I don't want to assume or narrate PC actions, I want to narrate outcomes. This doesn't make my method superior to yours, it just makes it superior for my table. I believe yours works for your table just as awesomely.
Also, both of the approaches above were lifted straight from my last session. No contact poison traps, though.