Since the Schwarzschild radius is proportional to the mass, it is probably better to note that the maximum entropy of a black hole seems to scale with mass squa

Since the Schwarzschild radius is proportional to the mass, it is probably better to note that the maximum entropy of a black hole seems to scale with mass squared, instead of being proportional to the mass as in an ideal gas. But this can sort of be understood by noting that ( using a really badly flawed model of black holes) the minimum energy states are all occupied and to add matter, it needs to sit at a energy proportional to the mass of the black hole. Additionally, arguing about black holes assumes that we can not get any information out of the computer.