C is super close to the hardware in that it works exactly like the abstract C machine, which is kind of a generalization of the common subset of a lot of machines, invented to make it portable, i.e. viable to be implemented straightforwardly on various architectures. For example pointer provenance makes it work on machines with segmented storage, these can occur anywhere, so there is no guarantee that addresses beyond a single allocation are expressible or meaningful.

What makes C feel free for programming is that instead of prescribing an implementation paradigm, it instead exposes a computing model and then lets the programmer write whatever is possible with that (and also what is not -- UB). And a lot of higher level abstractions are quickly implemented in C, e.g. inheritance and polymorphism, but then they still allow to be used in ways you like, so you can not just do pure class inheritance, but get creative with a vtable, or just use another vtable with the same object. These are things you can't do when the classes are a language construct.