Yep. I believe there has to be at least one other person present, besides the priest, because the Mass is a public, not a private event. If one believes that the Eucharist brings blessings and grace into the world, and it is the reason God instituted the Church why would any day go by without it? The Mass has greater benefits for the world than just for those physically present.
SD
In addition, that extra "person" can be valuable as a deterent to crime by the priest.