There are hints that the memory capacity needed for transporter patterns is massive even for future technology.
The assumption that all electronic memories are digital and essentially stable over an arbitrary amount of time, in the worst case by making a perfect copy (also, the assumption you can always perfectly copy them!), is newer than most canon-defining ST material.
In the 1960s, going digital when not needed would likely have been a somewhat absurd notion for an engineer even when imaging technology hundreds of years into the future.
--- What follows is real life electronics geekery, for comparison ---
Even in the 1960s to 1990s, finding unquantized ANALOG signals (that are subject to degradation in storage in some way or another) to be the most economic storage encoding was common. There were audio and video tapes, one-line glass-stick delay line memories in PAL televisions and VCRs, analog image stores like Radechon tubes or DVBST displays in professional applications (jam-proof RADAR, 1970s computer graphics terminals, fast data acquisition), long-persistence phosphors in radar CRT screens, bucket-brigade analog delays (in 1980s musician's delay units), analog CCDs (in high speed data acquistion), semiconductor based but ANALOG audio storage microchips (eg the ISD1016 series). All of these provided a MORE economic solution than quantizing and digitizing, then storing digitally on a medium that could have held more analog data, then converting back to analog, the data that needed storing. Note: quantizing = translating a real-life measure into something that can be expressed as a writable number. Not all digital signals are quantized (eg a PWM signal might not be), not all analog signals are truly unquantized (modern flash memory for SSDs and USB sticks often use a kind of quantized analog format internally).
Even many (not all!) real life digital storage systems rely on cancelling decay effects by regularly replacing the data with a perfect copy for the data to last. DRAMs used in modern computers do. Mass storage systems like HDD or SSD only do so accidentally and occasionally. 284
Anything that can store a lot AND very fast is likely to need it. Unquantized data can neither be kept truly perfect for ANY length of time, nor can any copy of it ever be perfect (the ever-present noise will see to that).
Also, digitizing a very large amount of data will always give you a timing disadvantage - think of a real life camera sensor. While it can capture a, say, 12 megapixel (ca. 40 megabyte, assuming 3 channels a 8 bits) image at a 1/10000th second shutter speed (actually, most camera shutters don't work quite that way, but that is irrelevant here) - it is usually not capable of digitizing and transferring into memory all of that image in 1/10000th second (which would need a bandwidth of 400 gigabytes/second. Which would even today be an extra tall order, above what would be economical in the average camera). Using an analog signal would seemingly land you in similar trouble here - but in both cases the solution would be "use more parallel channels" (eg all rows or columns in parallel on a wire each), and working with analog end-to-end here could still prove the more cost effective solution if speed but not permanent storage was desired (say, 2048 100MHz video channels vs 2048 equally fast 8 bit flash or SAR ADCs. Both are nightmare fuel.).
In something (eg a living being) that moves internally on all levels, accepting timing skews by not imaging everything at the same time won't go well.
Even today, a system that would need short-term data storage capacity beyond what is possible/economic in a digital way would be likely implemented in an analog manner at the very frontend. 284