This is a cool technical feat, but I am almost sure that id attempted this and realized that it just was not ever going to sound very good. The PC speaker sound effects are bad enough (which is to say "as good as they can be, but still bad") and sound "cheap", and adding beep-speaker music on top of that would just result in a noisy mess - as evidenced by the video.

The beep-speaker music in Commander Keen was good and fit the theme of the game - but to keep the environment of Doom and the dark and moody feel and not be limited to the dulcet tones of a tiny piezo buzzer was a design decision, not being lazy.

Note that they could have supported Disney Sound Source / Covax Speech Thing style audio (they did in Wolf3D and Keen) but skipped that as well, likely for the same reason - it would have sounded like murky hollow garbage.

You can email John Romero and ask him, he responds to emails - my guess is that he will say "yeah we considered it, it sounded bad, we abandoned the idea" not that they were lazy. If you read about the run up to Doom's release, and the amount of crunch time they were putting in, they were anything but lazy!