There's been ongoing debate about the effectiveness of masks to prevent the spread of the influenza virus for years now. There were a lot of studies after the H1N1 pandemic since mask wearing was "recommended" but to my knowledge no state or federal mask mandate was put in place.

Here's a paper from 2010 after the H1N1 pandemic.

Face masks to prevent transmission of influenza virus: a systematic review
https://www.cambridge.org/core/journals/epidemiology-and-inf...

Our review highlights the limited evidence base supporting the efficacy or effectiveness of face masks to reduce influenza virus transmission. An important concern when determining which public health interventions could be useful in mitigating local influenza virus epidemics, and which infection control procedures are necessary to prevent nosocomial transmission, is the mode of influenza virus transmission between people and in the environment.

The interesting thing is everything they recommend, we've adopted during COVID, including physical barriers and front line workers additional PPE equipment:

Physical barriers would be most effective in limiting short-distance transmission by direct or indirect contact and large droplet spread, while more comprehensive precautions would be required to prevent infection at longer distances via airborne spread of small (nuclei) droplet particles [19]. In healthcare settings, stringent precautions are recommended to protect against pathogens that are transmitted by the airborne route, including the use of N95-type respirators (which require fit testing), other personal protective equipment including gowns, gloves, head covers and face shields, and isolation of patients in negative-pressure rooms

There's five additional studies referenced in the MedPub doc:
https://pubmed.ncbi.nlm.nih.gov/20092668/

A current Danish study concluded masks don't reduce the spread of the virus:

Effectiveness of Adding a Mask Recommendation to Other Public Health Measures to Prevent SARS-CoV-2 Infection in Danish Mask Wearers
https://www.acpjournals.org/doi/10.7326/M20-6817

In this community-based, randomized controlled trial conducted in a setting where mask wearing was uncommon and was not among other recommended public health measures related to COVID-19, a recommendation to wear a surgical mask when outside the home among others did not reduce, at conventional levels of statistical significance, incident SARS-CoV-2 infection compared with no mask recommendation.

People are already debunking this Danish study but here's a CDC study showed even when people do wear masks, they were still getting sick:

Community and Close Contact Exposures Associated with COVID-19 Among
Symptomatic Adults ≥18 Years in 11 Outpatient Health Care Facilities —
United States, July 2020
https://www.cdc.gov/mmwr/volumes/69/wr/pdfs/mm6936a5-H.pdf

In the 14 days before illness onset, 71% of case-patients and 74% of control participants reported always using cloth face coverings or other mask types when in public,” the report stated.

In addition, over 14 percent of the case-patients said they “often” wore a face covering and were still infected with the virus. The study also demonstrates that under 4 percent of the case-patients became sick with the virus even though they “never” wore a mask or face covering.

Personally I feel like masks aren't stopping the spread mainly because people either use one or two masks continually without cleaning them daily, or put them on dirty surfaces thinking its ok and then putting them back on, or simply not wearing them over their nose. Masks would probably be effective if people wore them properly and only used them once. Hoping 300 million people all follow those simple rules is a bit hopeful to say the least.