If I want to maintain some objective measure of improvement by keeping track of the time it takes me to do a 40-km round-trip, why is it important to not do a time trial every time (riding every other day), but to vary the workout by introducing longer and shorter trips, and, particularly, to often do the 40-km round-trip at a leisurely pace?
Context and Unlikely Answers:
I have no intention of racing. I'm using time trials as a loose measure of progress mainly because other objective measures (maximum heart rate over the trip when completed in less than a given time; the much more complicated oxygen efficiency measurements) are not quite so straight-forward.
I don't see the parallel in other sports. For instance, 100m/200m sprinters would not practice by running marathons, nor even 1/10th of marathons.
A tennis player who wants to become a better player does need to play leisurely often (with less challenging partners, for example), but that's because the reflexes then improve, making tougher games more easily winnable (by instinct). Improving reflexes is important in cycling, for things such as avoiding falls, but it's unclear why they might help with time trials.
It would be nice to understand what exactly happens when one rides at a leisurely pace, that eventually improves time trials. Do, for example, glycogen stores in muscle cells become gradually capable of storing more (glycogen), hence enabling a more intense workout during a time trial?
Like all good answers, what Michael wrote generates many more questions to help us increase our understanding of the "why" part:
If you've gone to any aerobics class, you'll have noticed that it's a very bad idea to maintain your heartbeat at 170 and immediately leave the studio with a heartbeat dropping down to 70. The workout will take a heavy toll on your body. Instead, it's important to slow down gradually to return your body to the lower energy state. Is something similar happening with cycling? If true: Suppose, for example, that I aim instead for an intense 10-km round-trip (every other day), but do not return until I have cycled 30 more kilometers at a leisurely pace. Does this also count as "periodization"?
Is the idea to simply keep moving at lesser power? Suppose I have a rowing machine sitting unused, or suppose I dabble (also willingly) with tennis. Can I use these alternative activities as the "low power" activities—during rainy days for example? In other words, do the base kilometers really have to be cycling kilometers, rather than running on the court or (virtual) rowing kilometers?
What if I'm not at all aiming for a (yearly) race day? These Tour de France cyclists look like they're a different breed of humans anyway. I just want to maintain a regular, gradual, and possibly very slow, level of improvement. Can I set up my own monthly race day? Is that inherently sub-optimal than a yearly race day? (Or, really digressing, is one yearly race all that the human body can aim for? In particular, do TdF cyclists use the Giro and the Vuelta as merely practice rides? Do they save their real energy for the Tour?)
If you live in Southern Italy and are enjoying cycling year round, you may not quite appreciate the frustration of those of us who have a far shorter season during which to enjoy the thrill. You may not even fathom why we sometime have to think about other than cycling.