Starting Strength feels like a low-volume program because it uses a powerlifting template to push mostly the squat as far as possible, with the goal of turning scrawny young men into thick young men ready to play sports like American football. The template works pretty well for other people and other purposes but
"too weak to be on the field safely" -> squatting 405 is its origin story. To this end, it prioritizes escalating intensity over volume.
It does that quite well with nine progressively heavier squat sets of five per week, plus a short list of other barbell exercises with a high return on investment. Done properly this becomes a grueling challenge that gets the trainee well acquainted with a progressive resistance approach to lifting. (This is far more important than the physical effects, the argument goes, because focusing on adding weight to the bar according to a schedule is a more effective template than a more traditional bodybuilding approach based on momentary muscular failure.)
Once the centrality of pushing the squat is understood, it's clear why Starting Strength doesn't have more volume: adding sets does not contribute to this goal. It is also clear why it's a bad idea to "just add volume" to the program: you will not have a good time with the rapidly increasing weight on the bar. Squatting three days a week, with a little more weight on the bar every single time, is more than enough signal to inform the body that it must grow to adapt to this stress.
People who add extra sets to the program will find themselves spending their recovery budget on that additional volume rather than on the ever-rising intensity of more plates on the bar. This is often unpleasant to experience firsthand, as the discovery comes to you underneath a bar you can't lift.
Plenty of programs accept these limitations and pick a different rabbit for the beginner to chase. For instance, they may reduce squat volume and increase upper-body volume, like Greyskull LP. Or, they may vary the rep ranges in more exercise-targeted sessions, like 5/3/1.
In contrast, the appeal of Starting Strength is in its plain simplicity. This doesn't just make it easy to understand. Its simplicity resists people screwing with it. More complex programs are more amenable to tuning and fiddling, which is often compelling but not optimal for the beginner who knows little — and can lift less. When running Starting Strength the goal is clear: add a little weight to the bar on a frequent schedule. Everything else — the sets of five, the limited exercise selection, the relatively few sets — is in support of that.