Because that latter effect you can build a huge tolerance for, you had to stay off of caffeine for everything but tournaments.
Put another way, you can alert the body and the mind but that doesn't necessarily lead to a high quality performance. Feel better is not the same as scoring more points.
I've done a little research on caffeine, and as far as wakefulness goes (not touching the other effects here), it works by binding to the same protein receptors the body uses to decide if it is tired. Body unable to get signals that should trigger a feeling of tiredness == Body not conscious of being tired.
BUT the body responds by producing more of those receptors, making it more likely that it will start getting signals of fatigue even when the signaling proteins are at a low concentration. Thus, regular caffeine takers will find they need caffeine to feel a "normal" level of tired. It takes roughly 2 weeks without caffeine for a regular caffeine taker to achieve a no-caffeine level of such receptors.
Now, how much of the above is pseudo-science? Great question. FWIW, when I did the research the sources seemed credible enough (naming actual proteins, referring to actual studies, not just giving me animated drawings and hand-waving details) and it at least correlates with my anecdotal data - I don't use caffeinated drinks or supplements as a normal rule but do use them for special events (unusually late night/early morning) and have found the wakefulness effects to be effective unless I slip up and get too lax in my definition of "unusual". I also never thought caffeine was a big deal ( I never knew withdrawal symptoms, for example ) until I stopped using it as a general rule and my sleep improved notably. That said, my sleep quality is generally terrible so it doesn't take much to improve it.
I ask because I tend to feel that less caffeine makes me feel "lighter" (so to speak). But I haven't tracked it closely. It's more a general pattern that I think I'm seeing, but perhaps it's wishful thinking plus some bias?
So if they drink some 30 minutes before a ~2.5 hr game, they've got 3 hours post-game. Which seems reasonable: an hour for interviews / meetings, some travel, settling in, then normal sleep.
At the NBA level, they're definitely not deficient on post-game recovery and nutrients either.
The U.S. has 6 time zones, but Hawaii/Alaska don't have NBA teams: Relevant time zones are Pacific, Mountain, Central, and Eastern.
Don't get me wrong, I love coffee. However, it may be more accurate to say that all of these people (including the athletes) are using caffeine to medicate their chronic sleep deprivation, which may be at least partly caused in the first place by caffeine consumption.
NBA basketball players are in a tough position because they often need to peak between approx. 7-10pm (local time), and they frequently travel between 4 time zones. Most individuals would be naturally winding down alertness during those hours, even with good sleep patterns.