Take this for an example...
I agree, a new monument stair should coincide with an accessible route and per IBC 1104.5 "Accessible routes shall coincide with or be located in the same area as a general circulation path." Obviously though, a monument stair cannot provide an accessible route; stairs are not a component of accessible routes and a ramp, lift, or elevator is needed.
However, a monument stair would likely be an interior exit access stairway. In most cases, these stairs are not part of the MoE. They may be used during a building evacuation, but are often not a part of the marked/designed MoE. The monument stairway is often in addition to the required MoE.
Therefore, as the monument stair is not part of the accessible MoE required by 1009.1 (posted above). However, if it were, then it would possibly require an area of refuge per 1009.3.3. A number of exceptions exist, but it is really not necessary in examples such as Jar put in the OP where two exit stairways are provided.