For me, the canonical UB example is a buffer overflow. No matter how you define UB, in practice a buffer overflow can result in for example, a system crash or - given appropriate very specific input data - encrypting all the files on your hard drive for a ransom.
Requiring compilers to restrict UB to something similar to unspecified behavior (where the behavior is not specified by the standard, but a C implementation must pick a behavior and document its choice) would require C compilers to prevent arbitrary code execution given a buffer overflow in C code, i.e. ensure that a buffer overflow in C code does not ever result in actual buffer overflow on the physical machine. This seems implausible to achieve - given the tradeoffs chosen for C, once UB hits, it really is undefined as it can (not in all, but in some) scenarios result in executing absolutely arbitrary machine code depending on the data provided to the program.
On the other hand, if you'd just want to say that the compiler can't assume that UB won't happen for optimizations, then many optimizations are impossible because theoretical UB is literally everywhere where basic arithmetic happens because of the possibility of an integer overflow - if UB would be required to do "whatever the hardware does" then it means that you can't even reorder basic chains of arithmetic instructions and have to execute every operation in order as-written to have the appropriate behavior in case of overflow.
Requiring compilers to restrict UB to something similar to unspecified behavior (where the behavior is not specified by the standard, but a C implementation must pick a behavior and document its choice) would require C compilers to prevent arbitrary code execution given a buffer overflow in C code, i.e. ensure that a buffer overflow in C code does not ever result in actual buffer overflow on the physical machine. This seems implausible to achieve - given the tradeoffs chosen for C, once UB hits, it really is undefined as it can (not in all, but in some) scenarios result in executing absolutely arbitrary machine code depending on the data provided to the program.
On the other hand, if you'd just want to say that the compiler can't assume that UB won't happen for optimizations, then many optimizations are impossible because theoretical UB is literally everywhere where basic arithmetic happens because of the possibility of an integer overflow - if UB would be required to do "whatever the hardware does" then it means that you can't even reorder basic chains of arithmetic instructions and have to execute every operation in order as-written to have the appropriate behavior in case of overflow.