During Mass we pray for everyone, alive or dead, on earth and on purgatory, plus we ask the help from God and the saints... So why give a stipend to the priest so he can offer the Mass to one specific person that passed away?
Mass intentions don't have to be for the deceased, they can be for any person or intention really. And we do it as a courtesy, like tipping at a restaurant--we're not obligated to, it's just a courtesy to the priest. "The laborer is worth his hire," as the Gospel says. Some people will give a stipend as a courtesy to a priest who has performed a wedding or a baptism as well.
Ludwig Ott lists in his Fundamentals of Catholic Dogma (imprimatur from 1954) three distinct types of fruits of the Holy Mass recognized since the the times of Duns Scotus (c. 1266-1308) which are the general fruit (fructus generalis) for the benefit of the whole Church independently of the Mass Intention, the special fruit (fructus specialis) for those whom the Mass is said and the personal fruit (fructus personalis) of the celebrating priest and the faithful present. Herefore there is a distinct benefit to be gained from the Intention. The practice of offering Holy Mass for specific persons has a basis in Tradition as it is referred to by Tertuallian of Carthage (, Chapter 10*On Monogamy*), St. Cyprian of Carthage (, 2.Epistle 1) and St. Augustine of Hippo (, Book IX, Chapter 12*Confessions*).