Yep, that's the way how all LED tubes works.
Well, it is a row of LED chips, that is all it has common with the selfadhesive strips.
And for the direct light generation: That is physically impossible without high resistive losses in the chip structure.
The way the LED physics work, the photon energy as well as the junction voltage drop follow the band gap energy of the junction. So a 3eV blue LED has no other way than having 3V voltage drop when excluding the resistive drops on parts just carrying current to the main junction.
White light needs to be "assembled" from multiple spectral lines.
So a white emitter would have to consist of areas with varying band gap across the chip (that is perfectly possible to make).
But problem is, you will end up with essentially diodes with varying forward voltage all in parallel. And that means the current will flow only through the area with the lowest voltage drop (so the red section) and the rest will be dark.
So to make the current flow through all sections, you need to include a kind of ballasting resistances into the structure, to add the extra voltage to the lower voltage (red, yellow) sections in order to get the overall voltage sufficient to light the higher voltage (blue,...) sections. In order to maintain control over the color balance, there would have to be extra resistance with all of the sections. Plus the overall color will be heavilly current dependent (at lower currents the voltage drop across the resistors will get reduced, reducing most the current through the higher voltage, so blue, sections first before anything noticeable happens to the red), plus as typical with semiconductors, everything is strongly temperature dependent, so the optimal current for a good balance would have to exactly follow the LED chip temperature.
In total you loose majority of the input power in these ballasting resistance structures, so the overall efficiency becomes very low.
In fact LEDs using this concept were made, but because of all the drawbacks became obsolete even sooner than they ever ramp up.
Using monochromatic LED allows nearly no resistances, so no additional losses in the LED structure, plus being monochromatic it can in no way cause any color imbalance (when the rest is derived from its output).