The core tradeoff between an ice bath style tub and a chiller tub is upfront cost and convenience. A chiller tub costs more but holds your set temperature indefinitely with no manual ice runs. An ice bath style tub costs less upfront but needs regular ice top-offs, which becomes a real time cost if you're plunging daily.
If you plunge less than a few times a week, the manual ice-bath approach is often the more practical choice. Daily users tend to find the chiller pays for itself in saved time within the first year.