That is right.

While C like in many other places fails to define the correct behavior to avoid shaming the processor or compiler makers that fail to provide it, there are only 2 correct behaviors on overflows and underflows, like when incrementing the biggest number or decrementing the smallest number.

Both for signed integers and for non-negative integers, the 2 alternatives of correct behavior on overflows and underflows is to either generate exceptions or to saturate the result to the biggest or smallest representable number.

Wraparound is the correct behavior for integer residues, which are a distinct data type from either signed integers or non-negative integers.

While some people criticize C for making easy for careless programmers to make certain kinds of bugs, like access outside bounds, those are easily mitigated by using appropriate compiler options.

For me a much more serious defect of C is this confusion promoted by it in the heads of most programmers, who do not understand which are the fundamental integer types and which are the correct conversions between them, because C uses "unsigned" instead of at least 3 distinct types that it does not have, bit strings, integer residues and non-negative integers. More rarely, "unsigned" is used for other 2 types that are missing, binary polynomials and binary polynomial residues. All these 5 types must be primitive types in a programming language because all modern processors implement in hardware distinct operations for all 5 types, which can be accessed only through assembly language when these types are missing.

When I was building my computing stack out of x86 machine code I noticed that even if my high level language only had signed numbers (I'm still pretty brainwashed by C, which leads to the conclusions of OP), I still needed the ISA's unsigned jumps to deal with addresses (which can have the MSB set). So my big "insight" was to name unsigned comparisons "address comparisons".

https://akkartik.github.io/mu/html/mu_instructions.html