Revealing mistake: When Harry tells Marv to go back while they are climbing across the rope, in the shot facing them front-on, you can see Kevin in the background about to cut the rope. If you look closely this is not Kevin, it is his stand-in.
Revealing mistake: Towards the end when Harry walks up the frozen stairs, you can see it switches to a stuntman when he slips and lands on his back. (01:17:55)
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.