The plain answer
Is a head spa worth it? Start with what the hour actually contains.
Strip the marketing off and a head spa is a wash. A long one, at a basin that reclines so your neck is supported, with warm water running the whole time and somebody working the scalp, the hairline and the tops of the shoulders while it runs. Milbon products go on. A blow-dry finishes. The Signature tier runs 60 minutes and costs $80, and that hour is the unit most of this argument turns on.
So the value depends on what you were hoping would be different at the end. Clean, soft, freshly dried hair and a scalp that stops feeling tight — those are reliable. A relaxed hour in a dim room is reliable. Anything about how much hair you have, or what your scalp does next month, is not on the table.
Compared with washing your own hair, the difference is time and reach. Almost nobody spends twenty minutes on their own scalp in the shower, and almost nobody gets decent pressure on the back of their own head. Compared with an hour on a massage table at the same $80, it is a straight swap of which end of you gets the attention.
There is also the part people underrate: you cannot look at a phone with your head in a basin and wet hands nowhere near you. For some guests that enforced hour is most of the money's work, and the scalp work is a bonus on top. If the format is new, the full description of what a head spa is covers the equipment and the steps in order.