Interesting that they use such an underhanded phrasing, if their intentions are only good. Why not "do you know that your tail light is out?"
They don't need a confession to cite you for speeding. They already know if you were or not.
I've probably been pulled over 8 times in my life and only gotten two tickets. Who knows - this could have to do with my race or my demeanor - but in general I just try to act as honestly and apologetically as possible. I think most police officers are not trying to be jackasses, and the ones that are will ticket you whether or not you "fess up" or not anyway.
(This probably doesn't hold if you are carrying drugs or going 25mph over, but otherwise I don't think it helps to treat these interactions so adversarially)
There's far more on the menu and cops vary wildly in competence and intention.
I prefer the be respectful and say little more than necessary to excuse yourself route, all while keeping hands visible and making no sudden movements.
There's little to be gained by participating in a voluntary interview and prolonging the interaction, with a whole lot to be potentially lost, including your life.
A couple of times in a couple of decades of driving this has gotten me sent on my way with a warning.
If you're actually speeding or breaking some other traffic law and a cop pulls you over, you're likely going to get a ticket no matter what you say. The important question when determining how to handle it, then, is whether you are going to take the time and effort to fight the ticket.
If you're busy, have plenty of money, or just generally are inclined to pay the speeding ticket and move on with your life, then refusing to answer the cop is probably suboptimal. Your justification for not confessing is that if you do so, you "have no further defense for the speeding ticket." If you're going to fight the ticket, you're right and I agree with you. If you're not going to fight it, this has no value whatsoever.
If you're not going to fight it, then you shouldn't be optimizing for maintaining the best possible legal defense; rather, you should be optimizing for not getting the ticket in the first place. I believe that for most minor traffic offenses, you're better off confessing (and throwing in a relatable reason if you can pull it off).
Going with the lawyerly response is, in my view, more likely to get you a ticket than going with, "I think you pulled me over because I was speeding, and I want to apologize for that. I just left a first date with a girl who I have a feeling is going to be my future wife and got too excited. It was irresponsible and I should know better." Cops are people too - taking responsibility and making yourself relatable just might get you out of the ticket.