It is rather odd that you state that “Public domain software [ . . . ] is the only type that can be legally modified by the user for [their] own purposes.” However it is rather misleading that you don’t mention that Libre-software, software licensed with the General Public License(GPL) or Affero General Public License(AGPL), does just that, granted you can’t release the software to the public without also releasing the source code, which could go against someones purpose if said purpose was business related.
Mostly just pointing out that you missed Libre-software, or Open Source Software(OSS) for that matter, and that unless said software was licensed as AGPL and you aren’t acting as an Application Service Provider(ASP), or to a lesser