It depends a bit on your design intent. If you're making something for your own pleasure without much consideration for potential players, customers, then it's probably not really required. It definitely helps to iron out details and bugs. But that's something you can do on your own over time by playing it.
Otherwise? Playtests are absolutely invaluable.
If you are designing a product for many people to play. If you have a specific experience in mind, or if you have a specific audience in mind, you absolutely need to do playtests to make the best product possible. I come more from a video game perspective, but I've seen it again and again, it is an incredibly common mistake to think that you understand your market and your players well enough to take decisions in a vacuum. By playtesting, you will learn a ton of whatever you've designed, if it achieves the experience you had in mind, or if your audience enjoys what you've made. You can take different decisions following that, but decisions without data are not really decisions.
Playtests are also necessary for fixing issues. You might have all the right systems and mechanics to create the right experience and you might be pinpoint on what your audience is asking for... but there'll be typo, oversights, involuntary dynamics. Playtesting reveals you the monstruous underbelly of what you've created.
Now, as others have mentioned, there are definitely better ways to run playtests. And we could argue about the value of closed and open playtesting. I think it depends largely on your product, your goals and your means. But decades of cumulated experience in board games, videos games and all type of games have proven time and time again that playtesting is absolutely vital to have decent chances to make an excellent product.