How to Control standard rgb leds like individual addressable led

Other Hardware LEDs and Multiplexing
5

I'm just curious and want to know if we can omit ws2812 leds and build our own implementation

Basically no without a controller chip.
With the WS2811 controller you can have your own LEDs, and can wire up to three LEDs in series, but not common anode or cathode but LEDs where you can access each anode or cathode.

You can get PWM controllers where there are 16 outputs, then you can do five and a third RGB LEDs per chip. These are mainly I2C interfaced chips like the PCA9865.