But height does change in adulthood [0]. On average people living past 40 gradually lose height. At age 80, it's likely height loss will be >=2 inches. This loss is reflected in higher BMI even when body fat content hasn't changed. Average BMI increase isn't large, but think about a person losing 4 or 5 inches of height while maintaining body fat unchanged.
Self-reported height is generally greater than measured height. Adding 1/2 to 1 inch is common (per experience measuring height). "Height inflation" has modest effect on BMI but problematic in research and workup for medical procedures. In the latter cases, measuring height is necessary.
[0] https://www.uhhospitals.org/blog/articles/2024/10/why-do-peo...