How realistic would charging batteries with inductive power transmission be?
Efficiency could be a bit of a problem.

The induction power transfer is done through a high frequency EM field.  This transfer is not 100% efficient as it radiates energy in other directions (careful design could increase transfer efficiency, but you'll never get a perfect transfer).  The generation of the HF EM field consumes energy.

Therefore, you may get at best 80% \$^*\$ of the energy transferred from the battery to the device.

Then there is the cost.  It's not a cheap system compared to what is essentially a bit of metal that is used currently.

Combine the two and what is maybe a 99.999% efficient piece of metal would be being replaced by a complex circuit costing many dollars and reducing the efficiency to maybe 75%.\$^*\$

Then of course, if the device is switched off, the battery will still be consuming power in generating a HF EM field that is not being used, so there would need to be a way for the device to turn off the battery - and turn it on again without any power (most easily done with good ol' wires...)

So nice as it would be, I can't see it really being practical.

\$^{*}\$These efficiencies are just made up off the top of my head and not to be quoted as accurate.