The short answer is that they are too big and heavy for use on gas turbine engines. The rather longer answer is below.
Turbochargers are used in some high performance piston engines to increase the mass of air flowing into the inlet cylinders. This increases both the mass flow rate of air passing through the engine, and the overall compression ratio. The overall effect is an increase in power output.
But the turbocharging process also increase the temperature of the air going into the cylinders. This can reduce combustion efficiency, cause detonation, excessive wear and heat damage to the cylinders.
Intercoolers are sometime fitted between the turbocharger outlet and the engine inlet manifold, to reduce the temperature of the incoming air. They are simply heat exchangers in which heat is transferred from the charge air to some form of cooling agent such as air or liquid.
The main disadvantages of using intercoolers is increased weight and loss of pressure due to friction losses within the heat exchangers. They also waste fuel in that the heat taken from the charge air is usually discharged into the atmosphere.
In piston engines virtually all of the charge air is used for combustion, so the problem of excess charge air temperature is particularly severe. But in gas turbine engines only a tiny fraction (often less that 5%)) of the air is used for combustion. This leaves a large volume of air available for internal cooling. So the problem of high charge air temperature is less severe. This factor coupled, with the weight penalty involved in fitting intercoolers has meant that aircraft gas turbines do not use them.
Many modern ships employ gas turbine engines as their main propulsion systems. In these cases the availability of extra space (compared to aircraft) and the need for maximum fuel efficiency have led to the use of combined intercooling-recuperation systems.
The description below is taken from a Rolls Royce website describing the 25MW-WR-21, which is based on the Trent engine.
Compressor intercooling
The intercooler, located between the compressor sections, cools the intermediate-pressure compressor (IPC) air before it enters the high-pressure compressor (HPC). This reduces the HPC inlet temperature and therefore HPC work to deliver a significant boost in engine power. The intercooler also enhances recuperator effectiveness, as the inlet temperature is reduced thereby increasing exhaust heat recovery.
Exhaust energy recovery
The recuperator recovers and transfers heat energy from the hot exhaust, which is used to preheat combustion air, therefore much less fuel is required to reach the same power turbine entry temperature (PTET). As a result less fuel is used to achieve the same power.