I think the best piece of advice I've seen about that particular situation, is to see what the player says (the exact words, tone, etc they use) as what their character wants to say, or what they are saying in their mind, but then the roll determines what is happening in reality.
Maybe your discourse that you were insecure about actually stroke a nerve and performs unexpectedly well at convincing the target. Or maybe what you think is the perfect speech is falling completely flat because the tone is way off, or you are sluttering, or you are too close or too far from the other person in an upsetting way. Just like in real life: who hasn't had a joke we find hilarious in our mind be met with an uncomfortable silence and a quick change of topic? although that might be just me.
What I find it usually works best as a GM is to look at how the player describes their dialogue and if it's something outstanding, or something absurd, adjust the difficulty (slightly, so the stats stay the most important factor) accordingly. It's actually the same thing I would do when the players describe a battle tactic during combat, so it's not exclusive to social encounters.
I think what works best depends a lot on the system and the style of dialogue that it wants for itself.
With “Go then Roll” you are declaring what your character intends to do, which may or may not correspond with what it ends up happening, and the game master is the one responsible to detail the outcome looking at the result. The reason why it’s the most common option is probably because it allows setting the difficulty according to the details of the action described by the player, or in other words, it allows the player to influence their chance of success by doing things well (offering a good argument when persuading a target, attacking an enemy’s weak spot, etc), or badly (saying something ridiculously unconvincing, attacking an enemy in an obviously ineffective way, etc).
With “Roll then Go”, you just indicate the approach without adding details, roll, and then have the game master give you a result. Only after knowing the result you describe what actually happens. This prevents certain situations that, while they aren’t problematic for my understanding of “Go then Roll”, can be frustrating for some (like the character describing an epic attack, or giving a great speech, knowing that their chances are high, only to then fumble the dice roll and having their action fail). Here the difficulty depends exclusively on the character’s stats and the “what” of the situation, and not the details of the “how”, which can be good or bad depending on how you like to play RPGs. On the other hand, it allows the player to describe their successes and failures as they actually happen, and not only as their characters intend them to.
Personally, I tend more towards “Go then Roll”, and it’s how I have always played, but I can see how some games can take advantage of “Roll then Go”, and wouldn’t mind trying it sometime.
It heavily depends on the tone of the campaign and the players’ preferences. Some groups, in some games, enjoy death being a potential outcome, while others prefer for it to be completely out of the question.
There are also many degrees between both, like how much should potential death be telegraphed before making a decision that could end on it, or whether it should be relegated purely to an outcome of bad decisions and never caused by bad luck with dice.
My personal favourite is for players to make a decision when they are defeated: accept death (or retirement) and have their sacrifice improve the situation, or be left at the mercy of fate and have to face other consequences (easily worse than a heroic death, if the players care about the story and the world).