Cabin pressure is a differential pressure when you're talking about maintaining the same cabin altitude and flying at different altitudes. In other words, if you want to maintain a sea level cabin and climb to a cruise altitude, the amount of differential pressure (pressure inside the cabin vs. what's outside) increases, the higher you go.
When the structural limit for pressurization (or anticipated pressurization cycles) has been reached, that either limits the altitude of the aircraft, or any climb higher than that requires an increase in cabin pressure altitude.
The actual cabin pressure altitude isn't so big a deal so much as the rate of change. Generally we try to keep the climb and descent of the cabin pressure altitude to a comfortable 500 feet per minute, or less. Unless someone has a head cold, that's a good value for nearly anyone. If someone does have a head cold, they shouldn't be flying.
Pressurizing a cabin doesn't decrease stress on the fuselage structure. It adds stress. It also adds strength and rigidity if properly applied.
Think about the stress on even a small section of cabin. A door that's three feet wide and six feet tall has an area of 18 square feet, or 2,592 square inches. If a differential pressure is maintained of 6 psid, that's over fifteen thousand pounds of pressure just on the door. A 10X12" window has over seven hundred pounds pushing out on the plexiglass at the same differential pressure. Now think about the area of the entire pressure vessel; the airplane cabin is a big aluminum balloon that gets stretched with tremendous pressure with every pressure cycle.
I'm not sure that there's any great advantage to getting cabin pressure to sea level. Most people don't live at sea level. Take off in Denver or Salt Lake City and the cabin pressuring going down to sea level wouldn't be a big plus. Take off in Phoenix and the field elevation is already fifteen hundred feet. Why go down to sea level unless landing there? If landing there, the cabin pressure will be reduced to sea level prior to landing (we generally ensure that field elevation pressure is reached by 1,000' above ground during a descent to landing, and that the airplane lands unpressurized).
Aircraft structures are built just strong enough, plus a margin. Weight is a big issue in any airframe.
Carbon fiber offers certain advantages, but it also offers unknowns, and a conservative finite life due to some of those unknowns.
The entire fuselage isn't pressurized; the pressurized portion is called the "pressure vessel." Short of finding ways to strengthen the pressure vessel, what else is there to be done other than limit altitude? Differential pressure is the limitation; either strengthen the fuselage with different materials and construction at the same weight (new technologies), increase weight at the cost of payload, fuel, and performance, or limit the altitude of the aircraft. Those represent your options.
My question would be why it's so important to achieve a sea level cabin. What's the point?