I was raised by my lawyer dad to believe this, but over time I've refined my beliefs and think it's generally wrong.
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.