A luggage strap does two unglamorous jobs. It holds the case shut if the zip fails under pressure — the most common way an overpacked bag opens in transit — and it makes a black suitcase identifiable at a glance.
Ours adjust to fit cabin through to large check-in sizes, with a quick-release buckle so you're not fighting it at the carousel. If you want the case protected as well as secured, the luggage protection range covers covers and wheel guards.