Eebster the Great wrote:Also, given the potentially unconstrained growth of the Federation's resources, it seems like over the centuries the show spans, people should eventually have made plenty of memory storage. The size of a person doesn't increase, but the amount of stuff the Federation can have built over time could increase exponentially, and faster than even an exponential increase in population (thus, an exponential increase in per capita wealth). So it's not really an out.
There could be reasonable physically limits to this. Moore's law is not a law of nature, after all. It's going to taper at some point. And that point might be far away from "practical device that can store the molecular-level details of kilos of stuff".
As an analogy: I was just recently talking to someone who was a radar operator in Ye Olden Days. A radar screen was the stereotypical image from the movies. A round CRT showing sweeps, coupled through analog circuits directly to the output of the radar. With some capacitor-based tricks to filter strong reflections from the noise, and relying on the CRT phosphors to make the signal "linger" on the screen until the next sweep.
At some point, they introduced computers that stored the output digitally. Suddenly you could do new tricks, like extrapolate the course of a moving reflection.
The transporter seems similar to those old radars. It can just about manage the required data flow, but it requires specialized, single-purpose hardware. General-purpose computation channels are not good enough. So you can't do much "tricks". And general computation might have a limit that falls short of transporter capability.