As I feel a little less uncomfortable with "halo" orbits, with this question, I would like to explore the practical aspects, in particular those related to the design of the James Webb Space Telescope (JWST) operational orbit.
This (huge) spacecraft is scheduled to be launched this month, while its inception dated back to the end of the 90s (with an orginal target launch in 2007!). Its operational position will be in the vicinity of the Earth-Sun Lagrangian point "L2", about 1.5 millions km from Earth. For a vizualitation of the targetted JWST's trajectory in orbit around the Sun and around the Earth-Sun L2 point, see this NASA animation.
For an introduction to Lagrangian points (aka libration points), see What are Lagrangian points.
For an introduction to "halo" orbits, see Farquhar's classic "The flight of ISEE-3/ICE:Origin, mission History and a Legacy".
Note that there are other types of orbits in literature that are also connected to libration points, Lyapunov and Lissajous orbits. As far as I understood, halo orbits form a subclass of the Lissajous class. I propose that we focus here on this subclass (see sub-note below).
A previous question by @uhoh Are some Halo orbits actually stable? shed light on the existence of a subset of halo orbits that have the nice property of being (theoretically) stable. "Theoretical" means that we make simplifications to the real-word equations of forces, reducing the problem to a more tractable mathematical model. The model of interest is the so-called Circular Restricted 3-Body model (also designated as CR3BP, "P" for problem), which seems to be invariably used as a starting point for the preliminary mission analysis of halo orbits.
Intuitively, stability means that we do not need to spend any energy to keep a spacecraft from moving out of a prescribed (bounded) area. The magic of gravity suffices, in theory. In practice, it means we need to spend "very little", or at least much less than what we would have to spend had we targetted an unstable trajectory.
Was the JWST halo orbit chosen from a stable halo "template", and in "broad terms", what were the trade-offs between JWST's scientific mission requirement, orbital life-time and cost of station-keeping?
By "broad terms", I mean I would be satisfied with the results of an analysis comparing the Delta-v per year, amount of fuel embarked,... versus the "amplitude/size/excursion" (whatever this means, is up to you) of the halo orbit and its period. It would be nice if you could factor in the Deep Space Antenna Network constraints (how to maximize the visibility and link connections with Earth) and the launch window.
Related question Halo vs Lissajous, which station-keeping strategy and when?
UPDATE (6 Dec. 2021)
First, some hints on the approach they used to design the JWST orbit are given in the JWST User Documentation Home Page.
In particular (emphasis added):
The L2 orbit shape is not constrained, so torus orbits, halo orbits, or Lissajous orbits are acceptable and are determined primarily by the launch's time of day and day of year. This freedom in the L2 orbit design allows for multiple launch opportunities for most months and minimizes the velocity needed to get to orbit.
This corroborates well with the paper by Brown et. al. Seasonal variations of the JWST orbital dynamics . Thanks to @PearsonArtPhoto
This paper (published in 2015) provided (Fig. 5) an example of orbit realizations if the JWST had been launched in October 2018. The paragraph before the illustrative Figure reads:
The launch window is defined by continuous time intervals between 11:30 and 14:00 UTC each day for which all the previous orbital constraints are met, and includes margin for model uncertainty (e.g. propulsion system performance). The previous launch window analysis demonstrated that over half of the launch readiness period (October thru December 2018) provides viable launch opportunities that satisfy all orbit requirements. However, the geometry of the orbits varies significantly.