Over the years, this may be the biggest fear when starting a business using 1099s. I've seen this question come up everywhere from many different people, and I can see how it can be a cause of concern.
You can grow a small business using 1099s, and you can grow a huge business using 1099s. Look at Handy.com and how huge of a company they are. They probably do thousands of jobs per day, and they use 1099s. That should give you enough confidence that you shouldn't worry about your contractors stealing your jobs because it's not as big of an issue as many make it out to be.
Definitely, there will be contractors who take your clients, but it doesn't happen as much as you'd think. This will be a tiny issue if you properly prepare yourself and structure your company. There's always an option of switching your business model from 1099s to W2 employees as you start to grow. I see this all the time, but usually due to other factors and not because contractors are stealing their clients. On the other hand, I see people switching from employees to contractors as well. Neither business model is perfect, and both have pros and cons.