Skis absolutely do change with time and use.
Wood is used in lots of skis. Wood warps and stretches under loads and with moisture. My mother's old wood race skis had interesting racks for storage to preserve the rocker and camber. The wood waterskis I used to build all warped to unuseable after a season. Flipcore skis? Those might change a lot.
Foam cores get crushed with load. Delaminations with the skins and the cores also happen with loads. Resins can slowly creep over time - especially when heated. Fibers can break under load. Edges wear down. Metal in the skis gets bent. Certainly, skis do age.
While these factors do exist, skis are incredibly durable. Most skis grow stale by your impressions rather than any physical issues. Buy new skis because it is fun to ride new stuff. Despite lots of new skis, my favorite skis are still my beat up 6 year old Goodes.