I think it's pretty silly to remove the pins. Aside from assembly time I don't see any significant drawbacks though. I wonder if it could cause some reliability issues due to thermal expansion/contraction.
I don't have any issues routing out of the LM3886 footprint, so the pin cutting looks to me as a solution for a problem that doesn't exist.
The weak point in the pinout of the LM3886 is pin 4 (V-). You get the best power layout if all the power comes in from the pin 1 side of the LM3886, so cutting pins won't help you route to pin 4 as all pins in that end are used. The input and mute lines can be skinny traces and go easily between the pads.
That's not a recommended practice. Pins marked "no connect" or "do not connect" may connect to internal circuitry for testing purposes. This could be a thing of the past and I can't think of a single example where I know this to be the case for certain, but it is a possibility.
Tom