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I think that auto-brightness functions could have been implemented on analog scopes, but only to a certain degree, and it would be quite complicated. The operating and signal conditions can be very broad, so you would have to take into account a lot of variables like sweep rate, signal repetition (trigger) rate, holdoff, delayed sweep operation, whether it's in X10 mag, the number of channels active, the chop vs alternate modes, single-sweep mode, and so on. And that's just for the X-axis. What about the overall deflection velocity and extent, which also depend on the arbitrary vertical signals? You would want to know the actual peak to peak deflection, the risetime or other frequency content information, and the position on-screen - for every applied input signal channel, and make judgement about which parts are to be at the "right" intensity. That's a lot of stuff to figure out for the convenience, versus the simple way of having the user set it for overall appearance preference for given conditions. From the advent of the oscilloscope, all of this would have been nice to have, but is not very practical.
In a more controlled signal and display environment, it's a bit easier. One Tek product I know of that has some degree of auto-ness to this is the 577 curve tracer, which sort of controls intensity in proportion to the length of the horizontal deflection. In fact, the beam can set up to blank out entirely when the collector voltage approaches zero, so instead of a screen-burning bright dot at the origin, it just winks out, but will come right back as the voltage (deflection) goes back up. In this kind of instrument, the signal frequency and deflection ranges are are quite limited, and only so many operational modes are available, so an auto-intensity function is more practical and effective.
Ed