That is completely false. Look up "restrict" and there are many other contexts. BTW, "prove" and "assume" are different things. This is an old argument, which in a just world would have been settled by Dennis Ritchie's comments.
Prove and assume are indeed different things, but what the compiler is able to do is _prove_ the validity of the transform within the context of the C abstract machine.
Plenty of sibling comments in this thread show concrete examples of significant optimizations lost with alias analysis (and/or non-wrapping signed integers) disabled.
If the compiler is not allowed to assume that the source code is valid then very few optimizations are safe at all. Clearly that isn't what you want, so I suppose that you would argue that being able to vectorize something like 90% of all currently vectorizable loops in existing code isn't worth the cost, and instead compilers should be able to assume that anything my alias anything unless the programmer has manually restrict annotated every variable that is written to in a loop?
I expect in that world you'd see lots of code run needlessly lots slower, and lots of other code needlessly get slathered over with restrict annotations as restrict turns into a reflex because leaving it out results in poor performance so regularly... resulting in incorrect annotations and the miscompilation you were hoping to avoid-- arguably the worst of all worlds.