I think tha kind of thinking is extremely bad
I would think that under classic Christian theology (particularly in the west), all selfish behavior would be a result of the fall. Including children. Of course not everyone would characterize the results of the fall as total depravity.
Note by the way that most Calvinists (the main proponents of total depravity), while they consider things like selfishness in children to be results of original sin, also think all children are saved. But saved by grace, not because they're innocent.
Remember, total depravity doesn't mean that everyone is damned. Rather, it means that only by God's grace renewing us can we do anything towards salvation, including responding to God. It also doesn't mean that everyone is as evil as possible. Calvinists understand that non-Christians can do things that benefit others. It's just that these things always reflect imperfect motivation, and thus don't save anyone. The term "civil righteousness" is used to describe acts that are good for others, and that society and governments should encourage.
Most current Reformed people prefer the term "total inability" to "total depravity." Total depravity sounds like everyone is as immoral as possible. Total inability reflects what it actually means: that we are unable to do anything relevant to salvation on our own. God must first regenerate us, allowing us to respond to him.
[Because the question was about total depravity, which is a traditional Reformed concept, I'm describing the traditional Reformed viewpoint. This is not my personal view. This would appear to be the wrong forum for that.]