I think it has more to do with practicality. There have been a couple of incidents in the past few years where goalies got their gear in their team colors, and were traded. There were issues with the new gear not matching the new team. The goalies were forced to get new gear by the league/team, which wasn't broken in. This affected their playing style for a little while until it was broken in. I think Osgood was one of the guys affected by this, for example.
Going with neutral colored gear allows you to match any team, any time, no waiting.
Good point. This was more likely an issue a few years ago though.
Today, NHL goalies can have new gear sent to them pretty quickly, and for the most part, their gear is PRO STUFFED, i.e.; less stuffing. This makes them lighter and provides faster break-in. The pads do break down faster because of this, however, when you're not paying for your gear, you can afford to go through multiple sets throughout the year, similar to skates.
Also, it is possible to "paint" over pads. The paint does crack and chip off, however, it does the trick until new pads arrive.
Ex: Kipper with Calgary, still using his San Jose gear. The teal has been covered up.