Sugar is not there for sweetness
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The first job: letting the pectin bond
Sugar competes with pectin for water. With enough of it the pectin chains can find each other and form the network that sets; without it they stay in solution and nothing gels however long you cook it.
Pectin chains will not link while they are surrounded by water. Sugar competes for that water, which is what lets the chains come close enough to form the network you can feel on a spoon. This is why a batch that is short of sugar reads as undercooked no matter how long it boils, and why extension guidance lists incorrect proportions of sugar and juice among the causes of a soft set.
The second job: keeping the jar
The same concentration that lets the gel form is what makes the product hostile to spoilage, which is why the figure appears in both the texture answer and the safety one. One number is doing both jobs, which is why it cannot be lowered for taste without consequences elsewhere.
The same concentration that lets the gel form also leaves too little available water for spoilage organisms. That is the half people forget when they cut sugar, because the failure does not arrive on the day: it arrives as mold on a jar somebody opens in February.
So a low-sugar product is a different standard
The regulation treats it as one. Artificially sweetened preserves and jams have their own section with their own requirements, rather than being allowed as a variation on the standard product. If you are cutting sugar you are leaving one standard and entering another, and the label has to say so.