LEDs are not constant current devices. They are diodes with non-linear I-V characteristic curve.
The question of supplying LEDs with CC or CV power supply is only the question of efficiency and cost.
Most LED strips are made as a serial/parallel combination of LEDs with an added resistor for each segment, to get the desired current through the LEDs in a segment from a ~12V CV power supply.
You don't really have that much choice when it comes to LED strips. CC power supply would need to generate thousands of volts or you'd need a bunch of them. And that would be costly.