The electron beam experiences two forces. There is a set of high voltage plates that accelerates the electrons to a high velocity. There is also a set of coils which produce a magnetic field that steers the electrons. Due to the dimensions of the CRT, including the length that the electrons travel in getting to the screen, and the maximum angle that they need to be steered through in order to reach the top and bottom of the screen, they need a given velocity if the magnetic field is to steer them through the appropriate angle, because the magnetic force on the electron is related to both the magnetic field strength and the electron velocity.
From a practical standpoint, it is more convenient to build a "shorter" CRT device to ensure that it doesn't take up too much space in a room. This constraint leads design engineers to go for a larger maximum angle required to hit the top and bottom of the screen, which requires higher voltages and magnetic fields.