Introduction seems a bit off to me. Algebraic models of lambda calculi are known already, including treatment of binders and substitutions, and in a way which doesn't need combinators. E.g.: arxiv.org/abs/1904.00827

this is two different senses of the word "algebraic". the introduction to the paper is entirely correct! the lambda-calculus as usually constructed cannot be given as an equationally presentable class of algebras. the fact that you can give it a model in a cwf is distinct...

In fact, those photos argue that (and then rebut it). There are different meanings of "algebraic" in play. Universal algebra forbids languages from using binders; without this restriction, things get harder to study and model.