I think it is generally not a good idea to remove volatile from registers because writing/reading registers generally still has a side effect in addition to just changing the value.

For example, with volatile register accesses are never reordered (a different order may have different semantics).

Another example is that some infinite loops like while(1){REG=1;} would become undefined behavior (at least in C++) without REG being volatile. See: http://en.cppreference.com/w/cpp/language/memory_model (Progress guarantee).

In summary I think the only case where removing volatile from a register is where it has no specific hardware semantics at all - reading or writing has no side effect and the value itself does not influence anything.

Many registers are no different from a global 8-bit variables in that they will always contain the values which were last written to them. The compiler will be able to better optimize code which accesses them if they are not declared volatile.