Two reasons: Longevity and weight. Which really come down to just weight.
Airframes have a limited fatigue life, measured in flight cycles.
The main driving factor for airliner airframe wear is pressurizing and depressurizing them. Each millibar of difference between cabin pressure and outside pressure effectively consumes some percentage of the airframe's fatigue life.
Reducing the cabin altitude means increasing this pressure difference, and thus consuming more of the airframe's life. This could be compensated for with sturdier construction, which adds weight. It would also consume a little more bleed air, requiring slightly heavier packs, which, as well as weight, means a loss of efficiency.
Luxury business jets often maintain a lower cabin altitude, such as 4,000 ft. This eats into their flight cycles, so they can still be switched to the usual 8,000 ft for flights without the owner/VIP inside.
Carbon fiber has a much longer fatigue life, so CFRP fuselages can afford to lower the cabin altitude to 6,000 ft. This pressure altitude can also be maintained in other airliners at flight levels well below their ceiling.
The optimum compromise point is subject to a lot of debate. The highest cabin altitude that could be permitted is 15,000 ft, above which hypoxia-induced loss of consciousness can occur. The regulatory bodies have settled at 8,000 ft, so that's what the manufacturers targeted with most of their aluminum airliners, and that's where airlines prefer to run them even if they have a choice, to get more life out of their planes.