Visits, not spend, are the right mechanic
A barber visit is roughly the same price every 3–6 weeks. That makes a visit-based stamp card the right default. Points would over-engineer the math and confuse the customer.
A "10 cuts, 1 free" card works for the average 4-week cadence. The free cut costs roughly 7–10% of the customer's cumulative spend — well within the healthy band.