Why is a near rectilinear halo orbit a good place for a Lunar Orbital Platform-Gateway (formerly known as Deep Space Gateway)? Are there specific logistical and orbital-mechanical advantages over other possible orbits in cis-lunar space; other Lagrange point associated orbits or even high or elliptical lunar orbits for example?
The Deep Space Gateway would be initially placed in a near rectilinear halo orbit (NRHO) around the Moon.
In fact, they are the preferred option among other staging orbits by analyzing multiple factors:
EARTH ACCESS:
A study considering NASA SLS and Orion performances was carried out. Since SLS places Orion in a trans-lunar trajectory, Orion vehicle has to carried out orbital maneuvers to reach a orbit near the Moon, so the limiting factor will Orion's propellant load limitations. These makes difficult to access low-lunar orbits since an estimated budget of $\Delta V$=1250 m/s has to be enough for entering and leaving the orbit.
Analyzing the previous constraint, although for some epochs moon Keplerian orbits were affordable, they were discarded because they were problematic for continuous access. This reduces the candidates to orbits within the Restricted 3-Body Model: nominal L1/L2 halos (637-811 m/s), near-rectilinear halo orbit (NRO) (751-840 m/s) and distant retrograde orbit (DRO) (841-957 m/s).
LUNAR SURFACE ACCESS
This metric only measured transfer of the lander located at the staging orbit to a low lunar orbit (LLO) (the cost of descending and ascending from Moon surface to the LLO is assumed constant). Also, transfer time should be reasonable for the crew.
Obviously with this consideration, the preferred staging orbits would be Keplerian orbits near the Moon, but they were discarded by Earth-access. It is not difficult to see that between the 3-Body Model orbits candidates the NRO provides the best metric by terms of $\Delta V$ and time, if a polar LLO is chosen (note that polar orbits guarantees global surface access waiting the required amount of time).
ADDITIONAL CONSIDERATIONS
Considering station-keeping, for all the analyzed orbits, \Delta V budget per year was affordable (<10 m/s), so this was not a determinant factor.
When taking into account communications to Earth, 3-body problem orbits got another point for that since a direct line-of-sight with Earth is all time available. Communications with the Moon where most favourable (at percentage) with NRO and L2 orbits, although they favored one pole or one side.
Another preliminary analysis was done with thermal environment which also favored 3-body problem orbits, but it was not conclusive at all.
CONCLUSION
Staging orbit access from Earth with the Orion module discarded all the Moon Keplerian orbits. Among the considered 3-body problem orbits, the option that got most points was the NRO orbit.
My answer is entirely based on this nice paper about the subject: https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20150019648.pdf
