> All the attenuated live viral vaccines spread.
Can you point me to sources supporting that claim? I searched myself, and what I found says that our knowledge is limited to the polio vaccine:
"Little attention has been given to vaccine transmission, possibly because transmission is rarely measured and largely unknown in humans except for the oral polio vaccine. Whether transmission is indeed rare for other live vaccines, or has merely gone unnoticed, is not clear – polio vaccine transmission is accompanied by evolution to high virulence, creating problems that draw attention to transmission."
From "Transmissible Viral Vaccines", James J. Bull et al., Trends in Microbiology, January 2018. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5777272/