In the old days, you did have a problem.
Consider a sensor with max well capacity of 13Ke-, and rea-out noise of 13e-. DR is 60dB, or 10 stops.
Pair that with 12-bit ADC. Should be enough, right? Well, yes and no. You have 4096 gradations and you have to count up to 13000 electrons, so 892 and 895 will be the same to you. No big deal, since read-out noise means you can't really distinguish between 892 and 905, but, if you can't reduce that read-out noise, there's a small benefit if you go for a 14-bit ADC: you're getting better information about the image, and you'll be in a better position to try to average out that noise. Small, I know, but it's an improvement. if the 892 comes from a very unlucky 891 and 905 from a very unlucky 906, you're in a better shape if you can say there's a 3e- difference between them (when the real-world difference is 5e-), than if all you can say is that they're the same to you.
OTOH, if you stick to 10-bit ADC, then you clearly have a problem: your ADC-stepping will be added to your read-out noise. 892 and 904 electrons are the same to your ADC, but that 904 can come from a very unlucky 910, and that 892 can come from a very unlucky 886, and if 886 and 910 can look the same to you then you're in bad shape.