Edit:
It seems pretty useless as they essentially have no function (edit: to health), since the near-universal adoption of filters on cigarettes has not reduced harms to smokers and lung cancer rates have not declined [4]. And the color change is something that was added to make the filter to appear to be effective [5]:
> The tobacco industry determined that the illusion of filtration was more important than filtration itself. It added chemicals in the filter so that its colour becomes darker when exposed to smoke (it was invented in 1953 by Claude Teague working for R. J. Reynolds Tobacco Company). The industry wanted filters to be seen as effective, for marketing reasons, despite not making cigarettes any less unhealthy.
So trying to be rational here, they don't have any health benefits and are responsible for a large share of the microplastics in our ocean.
[1]: https://www.businessinsider.de/international/new-study-shows...
[2]: https://www.nationalgeographic.com/environment/2019/08/cigar...
[3]: https://www.nbcnews.com/news/us-news/plastic-straw-ban-cigar...
[4]: https://tobaccocontrol.bmj.com/content/20/Suppl_1/i10
[5]: https://en.wikipedia.org/wiki/Cigarette_filter#Colour_change