No, but they help a lot. Most new cyclists start with one pair of budget strapless shorts and then quickly realise, usually after they sag and slip down resulting in a cold lower back, that straps might actually be a good thing after all.
Cycling kit looks silly from an objective standpoint, but there's a good reason that all the cycling shorts in this guide have straps. They keep everything in the right place and prevent sagging, ultimately making you more comfy on the bike, which is what it's all about.