While having people find bugs might be one reason for an alpha release, it's not the only reason, or even necessarily the main reason. You might also want to see if people like a new feature, if the feature is well balanced, if it interacts with other systems well, etc. This is all useful information to gather before releasing a polished version to the general public.

If your alpha release is full of bugs, the type of feedback you'll be getting from users of the alpha is "this thing doesn't work" rather than "this thing is too easy/hard".