From the viewer's perspective, you see collision of balls and hence think of steel as an alternative, which is perfectly alright.
Let us now think how changing the balls to steel will have an impact on the player. (I'm assuming that while changing the material of the ball, the dimensions are retained)
The specifications of a billiard ball can be found here(specs), making the metal ball, $3$ times more massive than its synthetic counterpart. This factor alone influences the game in many ways.
- For getting the ball from point A to B, the energy imparted should be equal to the energy that will be lost to friction. $E = \frac{1}{2}mv^2=E_{lost\ to\ friction}$. By increasing the mass, not only are you increasing frictional resistance (frictional force is proportional to normal reaction), but also you are making it more difficult to impart extra energy to the ball $E \propto v^2$.
- This extra energy will have to be given by the player increasing his risk of having wrist injuries.
- To sustain the impact of the metal ball, the cushions have to be redesigned (which is not really a problem, I guess)
- Finally the paint. I've seen paint peeling off steel bars so I'm not too sure whether there exists some kind of paint which can sustain such high impact of billiard collision.
On a personal note, I think the part of billiard that I enjoy the most is watching a jump-shot successfully being executed(video). This would be even more difficult with the steel ball.