Ok, so why not slap on the double slotted flaps and larger tires on the 320 and offer a HGW version?
They did, its called a 321.
The question I would pose is why would you want to? Where would you put the extra Fuel/Bags/Pax?
As for the differences between the 320 and 21. the landing gear is beefed up, the tyres are bigger the, engines are more powerful, and it has what airbus call a "high lift pack" for the wing. double slotted flaps in other words. Also, while the aero foil section of the wing is the same with the flap retracted, the internal structure is not. The 321 has no outer fuel tanks, for instance.
As for performance, it struggles. Although due to the higher wing loading it is more stable on approach, But your approach speeds are in the high 140kts, mid 150kts with flap 3.