It could also be a programmer who is within their legal right to start their own company, but who doesn't want their current employer harassing or singling them out for it.

Further common situations involve trying to keep details out of the public record because they can be abused by bad actors; ones who may be looking to spam you, engage in a frivolous lawsuit, or personally harass you/your family. At least these are some of the scenarios mentioned by companies that do asset protection.

Edit: In regards to harassment, think about the abuse retail, fast food, or other customer-facing employees endure for perceived slights. It feels easy to understand why average small business owners would want privacy and to keep things in legal channels. Personally, I think the government knowing who's in charge (Corporate Transparency Act) is a good halfway point, but it's not unrealistic to be concerned about leaks or abuse with that system.