Are high velocity winds, or the lack of wind, the most common cause for low visibility?
Light or calm winds do not cause reductions in visibility, but stronger winds will generally be associated with better visibilities. Poor visibility is more likely in a humid, polluted air-mass than a clean dry air-mass. 

Reductions in ‘visibility’ or visual range are caused by the scattering and absorption of radiation by atmospheric particulates or aerosols. This attenuation of radiation will depend on the type, size and concentration of these particulates or aerosols. In a humid airmass water droplets can form on certain types of aerosols and these droplets can increase in size as humidity increases.  

Strong winds will tend to mix the polluted air near the surface with cleaner air aloft. This mixing will also create a more uniform profile of temperature and humidity in the lowest portion of the atmosphere. If there are light winds overnight, the air near the surface becomes cooler and more humid than the air aloft. The pollutants become concentrated in this cool stable layer of air near the surface. 

There are exceptions, namely advection or coastal fog. In far north-east of the U.K it’s not that uncommon to see fog with 20-30 mph winds during late spring and early summer.   

https://www.metoffice.gov.uk/learning/fog