There are many calls for, and proposals to include, some form of inheritance in Rust. Among other things, people have found that Rust is poorly suited to modeling HTML/XML hierarchies, retained mode GUIs, industrial simulations, code specialization, and some forms of video games. Inheritance
is a missed feature.
What is clear to me is that Rust does incredibly well without it, but wouldn't be hurt by having it. Most of the egregious sins of OOP are mitigated by having far better abstractions available in Rust. ML-style modules, ADTs with pattern matching, type classes, first class functions, etc. Much like scala, if you give them capable FP, OOP stops being abused and starts being used appropriately.