I’m going to answer this question from two different views, because honestly it depends.
First, the “proper” sewing view. Technically speaking, you should always use elastic in your swimwear. This is because the elastic serves an important purpose, and that purpose is helping the garment keep its shape. The actual fabric will stretch over time, but it’s the elastic that keeps everything in place. Elastic also helps the garment sit nice and flat so seams don’t roll over. On top of all that, having elastic in your swimwear looks and feels more professional, so if you’re selling swimwear that’s definitely something to consider.
Now I’ll discuss circumstances where you don’t “need” elastic. There are a few common complaints on why people don’t want to use elastic, and honestly it’s your choice. Sure, technically speaking using elastic is the correct way. However, at the end of the day it’s your choice.
Some people don’t like the feeling of elastic. It can feel constricting and some people just prefer a looser fit. There are others who don’t have the means to get elastic, usually because they can’t find any that ships to their country. Then there’s the people who aren’t worried about being proper quite yet, they just want to sew a bikini!
So I say just do what works for your situation!