You need a very stiff shaft if you want to run it from the top to the bottom with just two bearings.
Imagine bending the shaft and letting it snap back, while supported by the bearings. It will vibrate like a plucked string. The longer the shaft, the slower the vibration. The stiffer the shaft, the faster the vibration.
Now imagine the shaft turning, faster and faster, until it is going one turn in the period of that bent-and-sprung-back vibration. As you approach that rotational speed, the shaft will form a bend that gets bigger and bigger until the shaft fails. Even if it's perfectly balanced, the least vibration starts the failure which grows in positive feedback, pulling energy from the spin and putting it into bending the metal.
This was a big problem for gas turbines - to the point that, for years, there was some question whether they would ever work, rather than just tear themselves apart. The eventual solution was to damp the vibration and get through the resonance quickly. (Once it's spinning FASTER than the vibration period it's not a problem - until it reaches the second harmonic and does a DOUBLE bend, etc.)
I think there are solutions that involve more than two bearings, but I'm not an expert on this.