Private methods generally are a code smell anyway. If you have dozens of private methods in your class, something is probably wrong in your general design.
If your code is a collaboration of objects communicating via public methods, it's almost certainly going to be overly configurable (if it's using dependency injection) and thus be very hard to test every code path, especially given that consumers will probably be able to replace individual objects in the collaboration. It'll also be harder to understand, as objects which are broken out for modularity reasons show up publicly.
Minimizing public API surface is particularly important for versioning. If you don't control your consumers - if your API isn't fully internal to an organization and living in some kind of monorepo - then a big public API inhibits refactoring and feature extension as consumers take inappropriate dependencies on your implementation details.