Or maybe they would have logistical problems because they squander so much of their resources on tax funded bling and symbols.
Nah, all of their ongoing construction projects like that are basically rounding error compared to even the food budget.
The average American consumes a ton of food per year, figure that the average citizen of the Imperium is a quarter of that. A hive world of a hundred billion is consuming 50 trillion pounds of food per year. Given the levels of pollution and environmental decay on those worlds, and assuming that their recycling technologies are good enough to cover 80% of their food needs, they are still importing a trillion pounds of food per year. And that is exclusive of any packaging, spoileage, or other wastage. That is five hundred million tons of food imports. That is a third of real life Earth's total annual food production.
Compared to the costs of that, building one mega construction project per world per decade is literally such a miniscule expense that it basically amounts to petty cash. You probably spend more, as a percentage of income, on a Christmas tree every year than the Imperium spends on absurdly massive cathedrals.