Why should I insert steel plate inside bearings in elastomeric bearings?

Good question! After the addition of insert plate the freedom to bulge is restricted and the deflection is reduced when compared with bearings without any steel plates under the same load.
Actually as per procedure of elastomeric bearing act/ function as a soft spring it should be made to allow it to bulge laterally and also the stiffness compression can be increased by simply increasing the limiting amount of the lateral bulging.
In many cases in order to increase the compression stiffness of the bearing the usage of metal plates is made.
Once steel plates are included in the bearings the freedom of the bulge is restricted dramatically, also the deflection of the bearing is reduced as compared to a bearing without the presence of steel plates.
The tensile stresses of the bearings are induced into the steel plates.
But the presence of the metal plates does not affect the shear stiffness of the bearings.

To give the strength and balance to the structure by absorbing vibration.

For elastomeric bearing to function as a soft spring, the bearing should be allowed for bulging laterally and the compression stiffness can be increased by limiting the amount of lateral bulging.
To increase the compression stiffness of elastomeric bearings, metal plates are inserted.
After the addition of steel plates, the freedom to bulge is restricted and the deflection is reduced when compared with bearings without any steel plates under the same load.
Tensile stresses are induced in these steel plates during their action in limiting the bulging of the elastomer.
This in turn would limit the thickness of the steel plates.