Does drawing the current make the system stable or anything else

It's called magnetization current and basically, with the secondary unloaded, you can regard the primary as a big inductor and the resulting current that flows is the current defined by the primary inductance (aka magnetization inductance).

It's needed to induce a voltage into the secondary.

Of course you could use more primary turns (to make the primary inductance higher) and make this current smaller but, then it's a trade off between copper losses (more turns) vs "no-load" current (fewer turns).

_{Have you ever read "Goldilocks and the three bears"?}

Does drawing the current make the system stable or anything else

It's called magnetization current and basically, with the secondary unloaded, you can regard the primary as a big inductor and the resulting current that flows is the current defined by the primary inductance (aka magnetization inductance): -

\$L_M\$ is needed to induce a voltage into the secondary.

Of course you could use more primary turns (to make the primary inductance higher) and make this current smaller but, then it's a trade off between copper losses (more turns) vs "no-load" current (fewer turns).

_{Have you ever read "Goldilocks and the three bears"?}