How are unbalanced coaxial cables used for broadcasting TV signals without any problems?
But how come unbalancedness of coaxial cables have no problem in
  impedance balancing issues?


The beautiful thing about coax is that the shield shunts mostly all external electric field interference to ground and the inner wire is largely unaffected. For an external magnetic field interference, a subtle thing happens; the current that flows in the shield due to the presence of the field creates a volt drop along the shield and, due to near 1:1 coupling between shield and inner, that identical volt drop is present on the inner core. 

So, providing you use a differential receiver and the sending end has somewhat reasonably the same impedances to ground on both shield and inner, the differential receiver can reject the common mode interference.

If you do the math on the external fields produced by a regular signal sent down a coax and analysed the fields from send and return currents individually, you find that at all points outside the shield, the opposing magnetic fields exactly cancel to zero. There is no magnetic field outside a coax from a regular coax signal.

The impact of this is that the signal’s magnetic field is only produced in the gap between inner and outer shield. A repercussion of this is that the shield therefore has to have zero inductance. This is because the outer magnetic field is zero (aka zero induction) and the signal’s internal magnetic field has no effect on a tubular conductor (aka shield) hence, the shield behaves like an infinitely thick ground casing surrounding the inner.

That may be a little hard to swallow but if you go back to the theories of magnetic fields associated with a tubular flow of current, an external field is produced but no inner field. The reverse is entirely true; a magnetic field inside a tube induces no voltage along the tube AND, given there is no external field, the shield has zero inductance.

The upshot of all my rambling is that it works despite having a significantly unbalanced impedance regime between inner and outer shield. It’s not all that easy to immediately see I grant you so hopefully I’ve done it some justice.