Why nitrogen generation system is only present in centre tank only?
The inerting system was added to the A320 as a result of a new FAA regulation in 2008:

On 21 July 2008, FAA required
operators and manufacturers
to incorporate a Flammability
Reduction Means (FRM) or Ignition Mitigation Means (IMM)
on fuel tanks having a flammability exposure exceeding certain
thresholds [...]

(Airbus FAST Magazine 44)
Airbus found that only the centre tank was affected by these thresholds required by the FAA:

AIRBUS COMPLIANCE TO THE RULES
Airbus demonstrated that ‘only
the centre tank’ of some of its
existing aircraft has fleet average
flammability exposure exceeding
7% and is affected by the
requirements of the FAR Part 26.
There is no necessity to do any
modification on other tanks.
It concerns the following aircraft:

A320 Family,
A330-200, A340-200,
A340-300, A340-500, A340-600,
A300-600.


(Airbus FAST Magazine 44)
What exactly does fleet average flammability exposure mean? The FAA defines it as follows:

the percentage of the flammability exposure evaluation time
(FEET) each fuel tank ullage is flammable for a fleet of an airplane type operating over
the range of flight lengths in a world-wide range of environmental conditions and fuel
properties as defined in this appendix[, which] means the percent of time each fuel tank ullage is flammable for a
fleet of an airplane type operating over the range of flight lengths.

(FAA Advisory Circular 25.981-2A)
Since the centre tank is usually used first, it will spend more time empty (or almost empty). Fuel vapour is highly combustible (much more than liquid fuel), so the risk is significantly higher for the centre tank.

By the way, the system is not really a nitrogen generation system. It only enriches the nitrogen content of some HEPA filtered bleed air to reduce the oxygen content:

Air Separation Module (ASM) description
It is the core of the Inert Gas Generation
System. The objective is to reduce
the centre wing tank ullage O2
concentration to below 12%
during most conditions. Each ASM
is a semi-permeable hollow fibre
membrane bundle contained in a pressure
containment canister. This canister
is a cylinder with three ports. There is
only one ASM on the A320 Family aircraft,
two on the A330-200 and A340-200/300,
and three on the A340-500/600.


(Airbus FAST Magazine 44)