From Star Trek: The Next Generation onward, warp speed has a basically cubic scale from warps 1 - 9. But then, close to warp 10, it suddenly develops its own puzzling scale, as can be seen in this table.
In this scale, warp 10 is considered infinite, occupying all points in the universe simultaneously and therefore effectively teleporting instantaneously.
My question is why have this confusing scale? Why not have a uniform cubic scale? Was there ever any "official" explanation for this?
Clarification: I'm looking for why the writers decided on this, not the "in-universe" explanation.
Answer
If you're looking for the "canon-ish" answer for the change, according to the "Star Trek: The Next Generation Technical Manual" the scale was recalibrated in the 24th century. The old scale was calculated based on "observed" speed (much like our MPH/KPH), but the amounts of energy needed to maintain that speed could be vastly different from one moment to the next based on interstellar conditions and quantum drag forces. For instance you spend a few seconds traveling through a smallish eddy and it greatly reduces your velocity. Since such great distances were being covered in such a short time, a great deal of turbulence exists. Since the engines aren't actually fluctuating power to maintain a constant speed, the observed (averaged) speed was little more than a guess. I imagine this like driving a car at 6000 RPM over a surface that is at one second oil and the next sandpaper, with large rocks mixed in here or there. You could certainly figure out what your speed was for the last mile, but it may not be indicative of your speed for the next mile.
In TNG, the scale was changed to the amount of power required to transition from one warp plateau to another. The idea here is that it's easy (power-wise) to maintain a particular speed, but a power spike is needed to make that jump from Warp 1 to Warp 2. A larger spike is needed to get from Warp 1 to Warp 9. At that time, they decided Warp 10 was infinite power required. So all the "undiscovered" plateaus between 9 and 10 had to be squeezed in. I liken this to the metric system, where they decide a gram was a rather small amount of mass, but rather than recalibrate, people just decided to measure things in kgs.
Outside of canon, I recall an interview with Roddenberry. He put in a speed limit to keep writers from inventing more speed as the way out of trouble. You can see this a few times in the first season where the Enterprise tries to outrun things, but cannot (Qs grid springs to mind).
Edit: Just found online link to the TNG Technical Manual with a note alluding to Gene's decision.
Figuring out how "fast" various warp speeds are was pretty complicated, but not just from a "scientific" viewpoint. First, we had to satisfy the general fan expectation that the new ship was significantly faster than the original. Second, we had to work with Gene's recalibration, which put Warp 10 the absolute top of the scale. These first two constraints are fairly simple, but we quickly discovered that it was easy to make warp speeds TOO fast. Beyond a certain speed, we found that the ship would be able to cross the entire galaxy within a matter of just a few months. (Having the ship too fast would make the galaxy too small a place for the Star Trek format.) Finally, we had to provide some loophole for various powerful aliens like Q, who have a knack for tossing the ship millions of light years in the time of a commercial break. Our solution was to redraw the warp curve so that the exponent of the warp factor increases gradually, then sharply as you approach Warp 10. At Warp 10, the exponent (and the speed) would be infinite, so you could never reach this value. (Mike used an Excel spreadsheet to calculate the speeds and times.) This lets Q and his friends have fun in the 9.9999+ range, but also lets our ship travel slowly enough to keep the galaxy a big place, and meets the other criteria. (By the way, we estimate that in "Where No One Has Gone Before" the Traveler was probably propelling the Enterprise at about Warp 9.9999999996. Good thing they were in the carpool lane.)
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