I'm not sure what you mean about volume being "the weakest point". First, let me explain the point of the exercise:
In particular "how many bits can you hear?" is asking how many bits of the exercise, not of digital audio in general. I'm trying to make it easily identifiable, and even generously loud for a given bit level. By contrast, hearing tests I've experienced use soft edge sine tones and headphones emitting a calibrated level. That tends to leave you questioning whether you're hearing a tone or not when it's on the edge. With a harmonic-rich sweep, if you're not sure if you hear it, you probably don't.
The point of having the announcing voice (at the default output level) is so that a person knows how loud their system is. Not just to keep people from "cheating"—this is a personal test and I'm only asking "how many" rhetorically—I'm not looking for an answer from anyone. Also, if people are just going to keep turning up the volume as the sweeps get quieter, there is no point to the test at all. Lastly, I'm concerned that people will do this, and forget about it or have a system alert go off and blow out their system or their ears.
The point of this is only personal introspection. A lot of people say they can hear all the way down to 24-bits, other call for true 32-bit DACs apparently because they don't think 24 is nearly enough, usually without having any idea what -100 dBFS sounds like
on their system, at their normal listening levels.
So, I think my self-test is what it was designed to be. But I still like to hear and talk about what other people think are also interesting tests, so I welcome your thoughts. I just wasn't sure if you were saying you'd like to hear the first sweep ("5-bit") as a reference ahead of each subsequent sweep, or something else.