My understanding is it’s the physical barrier, not the carbon, that’s helping with this. The 0.5 to < 1 micron in size part of the filter spec in this refrigerator example.
My extensive sample size of 1 person with several refrigerators is that without the filter in good working order, the ice maker valve is likely to have issues that may lead to water dripping down and freezing the entire door shut, creating a huge mess in the process of resolving. Likely to occur while away for a week.
Using a slightly larger sample size with many K-Cup machines, using pitcher filtered water instead of tap water extends the life of the machine greatly.
*-All samples of unscientific size, conclusions not guaranteed. Sometimes you need a quick cup, don’t judge my coffee purchases. My other gear, while inexpensive meets most coffee snob guidelines. 
