Every music medium has that
Yes but there are subtle differences. On physical formats, the terms usually include the phrase “Unauthorized [whatever] is not permitted”, implying that if you have the correct license, it’s OK to record, broadcast etc.
OTOH online services just say it’s for personal use only - nothing to imply that you can use it if you have a license.
Some online services even have a separate site for “commercial” users - reinforcing the fact that the “consumer” site should not be used in public.
Tidal though have an agreement with Denon DJ (https://tidal.com/partners/denondj), so even though their “consumer” Ts&Cs say what they say, Tidal are aware of what their streams are being used for via the Denon DJ equipment. Tidal also has other partners that are either DJ software or hardware.