I respectfully disagree. Cheer is a different animal than any other sport, a different dynamic, and is perceived differently, for good or ill. Its the reality of the situation. It IS different.
You yourself have said that most parents have little to no understanding for the sport. That isn't true for most other sports. When you have parents who don't understand the sport they don't understand why their kid is cut. This is where you end up with parents on the warpath, and no matter how much transparency you have it WILL happen. It happens a LOT more in cheer than other sports because parents don't get it. Many view it as a club or activity, or even a popularity contest. The emotional attachment is much bigger than other sports because cheerleaders are so much more visible. Many people simply see it as a prestige thing and get disproportionately angry about it. Should this be the case? Nope, but its the reality of the situation.
Having outside judges isn't about having the guts to pick your own team, its about protecting yourself and your school from unjust accusations and the ugliness that comes with them