Dear Student ,
Cores are used to increase flux density (B field) in the secondary winding or, in other words, reduce flux dispersion. This increases electromotive force in the winding for the same applied voltage. While the ratio between the electromotive forces on the two windings is equal to the ratio of turns of the windings, that is not true due, among other things, to flux dispersion. Flux dispersion decreases power factor, also, you’d need a bigger transformer (more expensive) for the same voltage ratio.
Regards