In the past there have been comments made about filters because when they have been changed the user looks at them and found them not looking very pleasant, and assumed they might be unsafe. But it's more likely it's been doing it's job, and stopped what they saw from getting into their system!
To stop any of the residue caught by the filters from becoming a breeding ground the filter packs from the reputable companies should also have had a dose of bacteria inhibiting agents to prevent that possibility. Some cheap filter replacements may not have had the same protection as the OEM specifications.
As Buckman and Roger L have touched on above, if the filters are not changed in a timely manner things can start to go wrong. The dosing chemicals can become ineffective, and the filter might be fine to become a source of contamination, the filter could become physically blocked, but more frequently, the carbon granule retaining bag or screens break down allowing the granules into the caravans water system and that can compromise non return valves, mixer valves and the outlet grills on taps.
Most filters use activated carbon because it can capture a range of contaminants, including unpleasant tastes, like excessive chlorination, and others which might be a feature of some supplies. That's one reason why filter jugs are still popular.
Especially in the UK and most of the EU and other places that have mains water supplies the water does not need to be filtered.
Caravan filter systems have had their fair share of problems, some have developed leaks, others have been very difficult to change the filters. Some have been tucked away and difficult to reach, yet alone change.
And yes some problems are due to operator errors such as forgetting to change the filter on time, but some caravan manufacturers are also guilty of not making it abundantly clear if their caravan has been fitted with a water filter or not, and where and how to check or change it.