Here's why it's important.
When the bullet travels down the barrel, the barrel torques. This produces a "whipping" motion in the barrel. The barrel literally vibrates like a bell does. When the barrel is not touching anything, it vibrates pretty damn close to the same each time with the barrel in almost the same point of torque when the bullet exits the bore... The vibration is like the tone of that bell. Like a bell, when you lay it up against an object, the tone of vibration changes. the pressure on the barrel can change due to temperature, humidity, altitude, etc. as well as the set of the barrel against the object. This creates an inconsistancy in accuracy that is capable of having dramatic effect even at short distances.
Now, you can fully support a barrel as long as the support is constant and tight. There are supported barreled rifles out there that easily capable of 1/2 or better MOA. It's a lot easier to get the accuracy by free floating. You also get a significant weight savings.
For some people, the need for accuracy cannot be overstated. Law enforcement "snipers" may need to engage a hostage taker with only an eyeball exposed. The difference between a rifle that shoots 1/2 an inch at 100 yards and 1 inch at 100 yards could mean the difference between life and death to the hostage. They aren't shooting at people at 1000 yards, but they could literally be shooting at a target the size of a gum ball at 100. They damn well better have a rifle capable of doing it. 99.9% of them will want a free floated barrel on that rifle.