Couldn't that be overcome with a uC and buffer logic? Latch all the required pins inactive until sound output is required? Maybe I don't understand the issue.
The problem is two-fold:
1) A uC requires programming, so it will be more difficult for people to build their own. They not only need to solder a kit, but they also need to have the equipment to program the uC.
2) How do you determine when to mute, and when to unmute? (preferably you don't want to rely on some DOS utility, to maintain compatibility with booters, since early PCjr/Tandy games were booters).
Aside from that there's a decided anachronism and lack of elegance in using a microcontroller for such a simple 80s device.
I'd much prefer a simple discrete solution if one exists.
I personally think that just having an easy to access volume knob, or even a mute switch on the device would be good enough. Simple and cheap to build, and very effective.
Other than that, I have suggested using some kind of adder circuit, which generates the proper sequence of volume commands on-the-fly. Would probably be simpler and cheaper than a uC, and also true to simple 80s tech.