Although there should be only one intention per Mass, perhaps we should have a look at what the situation would be if this were imposed. When would we ever get a Mass offered for a loved one?
In my parish there can be as many as 20 people mentioned - some asking for healing or other intentions, some in thanksgiving, and, lastly, a number for the dead (named, or for the souls in purgatory). This is every day, two Masses a day Monday through Friday, Saturday morning, the Saturday evening vigil Mass, and four Masses on Sunday.
If there could be only one intention per Mass, it would take about 20 years to offer Mass, one per intention, for all the intentions now being offered.
In prior years (prior to VII), it was common for priests (with the permission of the person making the request for the Mass) to send these intention (and the offerings) to priests in mission territories. I do not think this is done now. Anyway, people want to be at the Mass and hear their intention mentioned.
There is no limit to the graces available from one Mass, so multiple intentions do not cause anyone to receive less grace because of other intentions being included. I think, mainly, the problem is the possibility of the temptation for a priest to become greedy for the offerings…