Transformer at no load
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"?