Why can cutting sugar make a cake dense instead of simply less sweet?

Answer: With less sugar, the batter's starch and proteins set earlier, before the bubbles have fully expanded

Sugar provides all of a cake's lift, so cutting it removes the rise entirely — Wrong. Creaming sugar into butter does cut air pockets into the fat, but the rise also comes from steam, from the leavening's carbon dioxide and from the trapped air expanding in the heat. A low-sugar cake still rises; the problem is that it sets before it has finished rising.

With less sugar, the batter's starch and proteins set earlier, before the bubbles have fully expanded ✓ — Correct! Dissolved sugar holds on to water and keeps starch from gelling and egg proteins from firming until the oven is hotter. That delay is what gives the bubbles time to grow before the crumb locks. Cut the sugar sharply and the structure sets early, at a smaller volume, so the cake comes out tight and heavy as well as less sweet.

Less sugar lets the flour build a much stronger gluten network that squeezes the crumb — Wrong. Sugar is a tenderiser: it competes with flour for water and gets in the way of gluten forming, so a sweeter batter has weaker gluten, not stronger. Reducing it does firm the crumb slightly, but a cake batter is far too wet and short-mixed to build a bread-like network.