> The lambda calculus is simpler, more well known, and more useful (it's a model of functions, instead of some made up rules about trees).
Lambda calculus is actually quite tricky; e.g. I've implemented it many times over the decades, both for fun and for serious applications, and have still never properly implemented capture-avoiding substitution (I've tried, but usually give up and reach for an existing implementation).
Also, notice that the tree calculus reduction rules are confluent, disjoint and branch on their left subtrees (similar to SK calculus). Hence they are also a "model of functions" like lambda calculus; or, alternatively, lambda calculus is also "some made up rules about [expression] trees".
Lambda calculus is actually quite tricky; e.g. I've implemented it many times over the decades, both for fun and for serious applications, and have still never properly implemented capture-avoiding substitution (I've tried, but usually give up and reach for an existing implementation).
Also, notice that the tree calculus reduction rules are confluent, disjoint and branch on their left subtrees (similar to SK calculus). Hence they are also a "model of functions" like lambda calculus; or, alternatively, lambda calculus is also "some made up rules about [expression] trees".