Of all the not-so-wonderful home situations various members of the Greasers find themselves in, Johnny's is by far the worst. His mom and step-dad are abusive alcoholics who hit each other and Johnny. His only escape from this horrendous home life to to "run away", and he spends many nights sleeping in the park rather than go home. Being cripple would trap him in that house with no means of escape. Furthermore, it would make him totally dependent on his mother (remember, this book was set in a time period where the world was not as handicapped accessible as it is today). It is hard to imagine that his mother would rise to the occassion. In fact, the added pressure of taking care of a handicapped son would only escalate the abuse directed towards Johnny.
I would think that this is because Johnny has a worse home life than anyone else in the gang. As the book says, "He'd have to stay in that house he hated, where he wasn't wanted..."
At home, Johnny has his mother and his stepfather. His stepfather beats him a lot and his mother thinks he is a pain. Imagine how much worse it would be if he were crippled. Maybe his stepfather wouldn't hit him any more (you hope) but imagine what his mother would think. She would complain all the time about how much of a burden he is.
That said, I think that being crippled would be pretty hard for anyone. Of the rest of the gang, I can't imagine what Dally would do if he were crippled since all he wants to do is fight...
Johnny's living situation was terrible. His parents were abusive and very violent towards Johnny. Even with good health and the ability to escape them, he still fell victim to their violence and verbal outpourings.
If Johnny were to have to live with his parents as an invalid, he would be socially isolated from the people he considers to be his family. He would have no means of escape from the "hell" that is his home. He would probably become even more abused because now he would be under their care all the time and they would resent him even more.