Separating a finished recording back into its component parts was impractical for most of recorded history. Software that does it reliably has altered remix and sampling work more than any change in the tools used to make music.
The mix was previously a one-way operation
Mixing sums many tracks into two channels, and the result contains no record of what was summed.
Anyone wanting to isolate a vocal needed the original multitrack session, held by the label or the studio and rarely released.
Remixers therefore worked from whatever stems a rights holder chose to supply, which meant remixing was something you were invited to do.
Separation is learned, not extracted
Modern separators are trained on large collections where both the finished mix and its component tracks are available.
The model learns what a vocal, a bass line or a drum kit tends to look like in a spectrogram, and reconstructs a plausible version of each from the mixture.
The output is an estimate rather than a recovery, which is why isolated stems carry artefacts around cymbals and reverb tails where the sources overlap most.
Access changed before quality did
Early separation was usable for practice and unusable for release, and the improvement since has been steady rather than sudden.
What changed the business was availability: the capability moved from research code to a menu item in ordinary editing software.
A remix that once required a label relationship now requires a copy of the record, which shifts the bargaining position considerably.
Rights did not move with the capability
Extracting a vocal from a recording does not create any right to use it, and the legal position is essentially unchanged from sampling.
What has changed is enforcement, because an isolated stem is far harder to detect in a new work than a recognisable sampled passage.
Rights holders have responded by licensing official stems more readily, on the reasoning that a supervised route is preferable to an unsupervised one.
The archive became the main beneficiary
The largest practical use is not remixing but restoration of recordings whose session tapes were lost or destroyed.
Separating a decades-old mix allows a muddy vocal to be rebalanced, noise to be removed from one source without affecting others, and mono recordings to be given width.
Catalogues that were commercially finished are reissued in a form that competes with new releases, which is a change in supply that the remix market feels directly.