Does this layout ever make sense to do?
In general, adding an inductor in series with a chip's power feed and not adding decoupling capacitors to ground (at the pins) is really bad. Just don't do this whether you split it into three or just have a common track.

Even if you add capacitance you have to ensure that any changes in the current taken by the chip do not suddenly produce resonance overshoots that exceed the chip's maximum power rails. I've actually done this recently. 

The inductor was upstream towards the power supply and I had a 10uF ceramic at the chip to ground. I was testing the board for short circuit survival on the output of the chip (a switching regulator). It didn't survive because when the short on the output was released, the current into the device dropped very quickly and created a big under damped sinewave superimposed on the power rail to the device. It didn't burn or fry but it never worked again.