Quite a few sole proprietorships are schedule C proprietorships. They don’t have an EIN. They just pay taxes through their SSN/ITIN. If there are forms that the company needs to fill out, or permits the company needs, they use their SSN. And if the sole proprietorship has to open a business bank account or get a loan, the SSN is also used. This doesn’t create perfect separation between business and individual, but it doesn’t need to. Schedule C businesses are essentially the individual themselves.
However, if a sole proprietorship wants to hire employees, this all changes. A tax ID isn’t just used for taxes. It’s also used as an Employer Identification Number. A sole proprietorship must get an EIN if it wants to hire employees. It will need this EIN for its hiring forms as well as to pay payroll taxes. Most sole proprietorships should consider getting an EIN regardless, as they are allowed to do so, and they may need one in the future.