Why is volatile not considered useful in multithreaded C or C++ programming?

As demonstrated in this answer I recently posted, I seem to be confused about the utility (or lack thereof) of volatile in multi-threaded programming contexts.

My understanding is this: any time a variable may be changed outside the flow of control of a piece of code accessing it, that variable should be declared to be volatile. Signal handlers, I/O registers, and variables modified by another thread all constitute such situations.

So, if you have a global int foo, and foo is read by one thread and set atomically by another thread (probably using an appropriate machine instruction), the reading thread sees this situation in the same way it sees a variable tweaked by a signal handler or modified by an external hardware condition and thus foo should be declared volatile (or, for multithreaded situations, accessed with memory-fenced load, which is probably a better a solution).

How and where am I wrong?

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