Again, I would say this isn't about good faith play. I imagine we agree that part of good faith play is following the rules. If the rules the DM sets before the players lead to what the DM considers "gaming the system," where does the problem actually lay? It's not with the players in my view - it's with the rule or the DM or both.I don't think it is going to be as common a result as you seem to be saying. Players, by and large, play in good faith and aren't out to break the game and make it less fun for themselves. But many are, in my experience, kind of scattered and spontaneous. The benefit of explicitly allowing them to ask about proficiency after the roll has been called for (as, again, the rules do) is to not punish them because it took them a sec or because they missed something or because the lightbulb went on after the fact. And it allows the GM to clarify and embellish the situation as necessary. No one at the table is a computer. The creativity is the point.
It's also not punishment to set clear rules and expectations and help players rise to that standard, if they need it. Your description about what you want to do precedes the call for a roll. After that, there is no embellishment. You can add a proficiency that fits the description you already offered, not one you choose to offer after the call for a roll. That is clear, easy to understand, and a constraint that fosters creativity, not stifles it in my experience. As a bonus, it doesn't lead to the "generally negative" outcome that was mentioned.