There are several factors to aircraft stability. But lets assume thar youre right on wing loading being the only one. Especially to wind.
Take a cessna 152. To increase stability and wing loading you cut half the wings off. Due to lower lift generated of smaller wings you must increase airspeed to fly same weight. By increasing forward speed vector, the ratio of side vectors decreases. Ie cross wind has less effect. Since that had desired effect cut them in half again. Will have to increase engine output to achieve minimum takeoff speed. But thermals and rotor will have less effect. But stall speed is higher, takeoff speed is higher, fuel use is higher, roll stability is lower, payload is lower. You better also will want to concentrate on flying than sightseeing
Paragliders are very stable. They get their stability by having center of gravity centered and much lower than center of lift. It causes a pendulum effect. Want a more stable paraglider, increase the riser length. But there comes a point it will be so stable that it wont turn and take off and landings become impossible.
Gyrocopters have several limitations. First they are high drag to lift. Fuel efficiency is lower than paramotors with same pilot weight and speed. They must have torque compensation of main rotor or they will roll as speed increases. Advancing rotor blade generates more lift than retreating blade on other side.
As for general avaition not being effected by thermals and rotors?? Have you never encountered turbulence while flying in a 737? Done a cross wind landing in small airplane? Talked to helicopter pilots about rescuing hikers in canyons when its windy? They are affected, they just typically dont fly near ground in those conditions
Paragliders greatest advantage, is size and weight. My paramotor wing weighs 4.8 kg or 11 pounds and can fit in carry on baggage on airlines. Just ordered an sp140 that can fit in the back seat of my electric car. I free fly mountains in ridge lift to fly without power. Do cross country flights in thermals without power. The disadvantage youre talking about is advantages to others