"One of the values written to memory" isn't really a thing when memory accesses can tear (e.g. because the values are 16 bytes large and are accessed using 8 byte memory ops). So it's not even necessarily about what would be lost, it's about what can be reasonably defined in the first place.
If you restrict yourself to relaxed atomic loads and stores -- i.e., memory accesses that are atomic in the sense that they cannot tear, but don't have much in the way of ordering guarantees -- then you do get "one of the values that had been written to the memory in the past".
Aside from memory tearing, one other issue is that you generally want to be able to rematerialize loads (i.e., in the face of register pressure, you may want to turn one load of a value into multiple loads instead of loading it once, then spilling to the stack and reloading from the stack). But when the compiler rematerializes a load, then you don't get "one of the values written to memory". From the perspective of the original program it looks like you get some weird superposition of values.
If you restrict yourself to relaxed atomic loads and stores -- i.e., memory accesses that are atomic in the sense that they cannot tear, but don't have much in the way of ordering guarantees -- then you do get "one of the values that had been written to the memory in the past".
Aside from memory tearing, one other issue is that you generally want to be able to rematerialize loads (i.e., in the face of register pressure, you may want to turn one load of a value into multiple loads instead of loading it once, then spilling to the stack and reloading from the stack). But when the compiler rematerializes a load, then you don't get "one of the values written to memory". From the perspective of the original program it looks like you get some weird superposition of values.