"Supply chain" has connotations of using metal chains to strongly anchor down things so you don't lose them. If a company has a supply chain, they feel in control of things in the chain.
"Dependency tree" implies vulnerability. A company that depends on something is at the mercy of that thing, and has little control over it.
This is a gross simplification, of course, but maybe there's a grain of truth here on why companies are so interested in supply chains instead of dependency trees.