Basically you want a virus that really is a vaccine. The current vaccines are far from perfect because apparently we don't know how to make them better. Expressing such a vaccine as a contagious virus would not better but would only create more risks.
Using "live" virus is a problem. For example there are two versions of the polio vaccine. The injectable uses inactivated ("dead") virus, and the oral uses weakened("live") virus.
Both are safe, but in the oral one the virus can go to another person and cause no problems, and then to another and cause no problems, and after like a year jumping hosts it can mutate and become dangerous. Now most of the the polio cases are caused by virus that mutated from the version of the vaccine. https://en.wikipedia.org/wiki/Polio_vaccine#Vaccine-induced_...
The number is much smaller that the number of cases before the vaccine, but it's concerning anyway. So they are trying to discontinue the use of the vaccine with the weakened virus, but the it's better when most of the population is not vaccinated. https://en.wikipedia.org/wiki/Polio_vaccine#Schedule
So ... probably the authorization and test necessaries to use a new vaccine with and attenuated virus are more difficult than a vaccine with an inactivated virus (or a vector virus, of mRNA, that also can't spread).