When it comes to Vinyl, then the vinyl itself is Analog. However, the Digital being converted into the Analog to press onto the vinyl itself is the problem. AAA is the beat there is as no algorithms took place onto the music itself.
Analog: "relating to or using signals or information
represented by a continuously variable physical quantity such as spatial position...."
That means, it's not a replica of the original, it's a
representation. It includes added information that was never in the original. These additions are the analog path's flaws, it's failure to accurately reproduce the original. The flaws are not small at all, all easily measured and heard.
By contrast, quantization produces a series of instantaneous accurate samples that can be used to precisely reconstruct the original, with accuracy limited only by the Nyquist frequency and to lesser extent, the number of bits used. PCM produces a replica of the original signal, with minimal flaws that are orders of magnitude below the level of errors in any analog recording system. Digital converted to analog is not a problem at all when cutting the master lacquer, any more than an analog recording is. The modulated groove has many, many physical limitations that must be considered, and the mastering process is strongly dictated by those limitations, regardless if the original master is analog or digital. The resulting lacquer master and playback system introduces further limitations and additional error signals.
Some people argue that the techniques to print the vinyls are considered algorithms, which is true. However the algorithms to interpret 0-1 binary Codes into an analog waves are different than the algorithms used as a printing techniques. The level of influences are also different.
The processes involved in cutting a master lacquer are not really fixed algorithms, they are highly variable based on subjective judgement and desired result, limited by the constraints of the medium. Those subjective judgements, processes, and media limitations are quite significant, with the subjective decisions being the single biggest influence on the result.
The process used to convert a data stream into an analog signal are a fixed algorithm, they are not variable at all, and there's no subjective judgement possible. Therefore, the impact of the D/A algorithm is zero by definition. But then, you take that analog signal and cut a lacquer using the identical processes used when cutting from an analog master, same subjective judgements, same media limitations.
The question of which is better can only be answered subjectively, unless the ultimate goal is perfect replication of the original signal. If that is the goal, digital systems are the only choice as released recordings are exact replicas of the master. This is never true in the analog world regardless of the media as all analog recording and reproduction systems and signal chains successively degrade the original signal with every step of the total signal chain.
If the ultimate goal does not include perfect replication of the original, and there is a preference for some aspect of an analog method, then the user will gravitate to that choice. The choice cannot be called "right" or "wrong" unless the goal is fully understood. Audio bliss can be achieved in any number of ways, with many different types of media. There exists in this world a group with strong preferences for the 8-track tape cartridge, probably one of the most technically flawed media types of the last half of the 20th century.
Regardless of how those side of debates are. It is as simple as this, the less processing = the better.
Less processing = the better = digital. You must understand that every step of the analog chain changes (processes) the original, desired or not. Such is not true in the digital domain.
Yes, analog has many flaws including distortions and noises. But this is the best statement I have seen “The real World is Analog!”
Analog is exactly what comes pouring out of every single digital playback system. That particular signal replicates, exactly (if desired), the original analog input signal. If you don't like the original, then it is perfectly valid to distort it in any way you like until it's to your liking. You can think of the analog/vinyl system as a big filter that's modifying the original signal in a way that some like. When combined with the visual and tactile experience (non of which exists with a digital system) the composite experience can be quite compelling. But so can listening to a replica of the original heard during final mix...literally, a clone of the master.