Because cafeine breaks down over time so your evening/afternoon coffee has a much bigger effect on your later sleeping attempts than morning coffee. I don't drink coffee at all so that does not apply to me but I can see the confusion in the GP and your response to it.

Correct, that's what I was referring to with the long half-life. The later you consume caffeine, the more likely it is to disrupt your sleep. A logical extension of that is the following: if you know that caffeine has a worse reward-to-harm ratio in the afternoon, and you consume it even though it might disrupt your sleep (assuming it does), you might be grasping for productivity straws. Alternatively, caffeine pretty much only has upside when it is consumed in the morning. It increases wakefulness and several academic studies found that coffee specifically improves your health (not sure how much of that is due to the plant material vs. the caffeine).