It was legal to record TV, using VCRs and DVRs, for time-shifted viewing, due to the alternative being that the content could not be consumed at all (at the time of the Betamax case, episodes were broadcast once, and generally not re-broadcast unless they were extremely popular, and were not available for purchase individually or even as part of a collection).

Today, there are a multitude of options for consuming TV content, and due to the (recent) creation of time-shifted licenses, the fair use justification for standalone-DVRs has mostly gone out the window (which is why they're not for sale anymore; for example, Tivo no longer offers standalone DVRs; Hulu, cable companies pay for time-shifted viewing).

As Youtube was always on-demand to begin with, the time-shifting justification for recording TV in the Betamax case never applied.