Audio problem: When Kevin is going through Buzz's private things he finds a picture of his girlfriend. Sickened by her appearance, he smashes the picture. But the smashing sound starts before he hits it. (00:22:05)
Audio problem: When Kate is riding in the truck with the Kenosha Kickers playing "Deck the Halls", drums are heard. When the drums are not heard, the drummer is still seen drumming.
Answer: I think it was a way to make leaving him "home alone" more realistic and understandable as opposed to absurd. Being perceived as a brat/pest and annoying to be around, it is (somewhat) conceivable that none of the family members would be eager to have Kevin by their side. This "frees" all of them from noticing that Kevin isn't with them. Everyone would just assume that Kevin is somewhere among them and each be glad they didn't have to sit next to him on the way to the airport or during the long flight.
KeyZOid
In addition to this, the movie is partially about Kevin learning to have more respect for others. He appreciates his family more as he spends more time without them.