What is the advantage of having the carrier component in AM unlike DSB-SC?

In DSB-SC there is no carrier component. In normal AM we have a carrier component. Is there any advantage of having the carrier component?

Thanks a lot.

Using older analogue techniques, it's easier to modulate AM than it is SSB. I assume the same goes for DSB-SC. It's easier to demodulate AM than it is SSB. Again, I assume the same is true of DSB-SC, though I am not sure of this.

The carrier is wasteful of power. Likewise the two sidebands DSB-SC are wasteful of power, as one is a mirror image of the other. Radio hams use SSB a lot, as its much more efficient in terms of both power and bandwidth than AM is.

To my knowledge, SSB was never used for commerical radio transmissions intended for the public. The reason would be that the receivers would have to be complicated to demodulate the SSB.

I know its possible to demodulate SSB on n AM receiver if you feed into the receiver RF at the carrier frequency. I remember building a VFO as a kid to do this, and I could hear the SSB, but it needed me to retune the VFO every time I wanted to listen to SSB on another frequency. A more senible approach is to apply the RF at the IF stages, so it only needs to be done once.

So I believe the advantages of AM over more elaborate methods is simply that's its cheap to demodulate.