The main problem here is you're trying to use a sensor that's approximately 1/4 the size of your pinky nail. A normal point and shoot uses one about the size of your pinky finger nail and a DSLR sensor is slightly larger than a stamp. So, imagine you were trying to recreate a painting standing 50 feet away, 20 feet away or 5 feet away. Now consider on top of this, the lighting is poor, because you're indoors, and nothing beats the good ole sun for giving the best lighting (outdoors). For the farthest away one (the phone sensor), you'd have to guess on a lot of the details, because they wouldn't be clear to you. The closer you got, the less you'd have to guess on. So half the problem is that your sensor is so small, its guessing at what is there.
Also there's a lot of electrical qualities about the sensors that can produce noise in your photos. High end DSLRs already do well in low light, because they have huge high quality sensors. The technology to bring that small sensor low light sensitivity up, is on its way.
As far as MPs go, bigger is not always better. I don't really feel like delving into any further. But I could hand you a 1million MP camera (if one existed), and possibly still take better pictures with a lesser one, because of the sensor size and quality.
Also, someone mentioned using flashes etc. I know it seems bright, but the flash really has a limited effect here, no more than a few feet...and the further you get away from the flash, the improvement it offers is going to decrease exponentially. So really, I wouldn't consider the flash the issue.