I’m glad you brought up the history of halitosis and marketing. In fact, the oft recommended twice-per-year visit to the dentist began as a pepsodent ad! It turns out that in low risk individuals, the frequency of dental cleaning and checkups did not improve oral health outcomes.

https://evidence.nihr.ac.uk/alert/dental-check-ups-every-six...

Now onto halitosis. Intra-oral halitosis is caused by volatile sulfur compounds and volatile organic compounds that are generated by microbes in the mouth: aka the oral microbiome. A number of studies have shown that halitosis is associated with specific bacterial species that have been shown to create these compounds both in vivo and in vitro. A good review on the subject is here:

https://pubmed.ncbi.nlm.nih.gov/32748883/

A number of clinical trials aimed at the efficacy of mouthwashes, probiotics, probiotics, lozenges have even been published. The general consensus is that mouthwashes offer temporary relief (through broadly decreasing microbial burden), and some probiotics are effective long term, but there is still much to uncover in this space as community dynamics of the microbiome are complex.

https://pubmed.ncbi.nlm.nih.gov/30834725/ https://pubmed.ncbi.nlm.nih.gov/27508274/ https://pubmed.ncbi.nlm.nih.gov/31799694/