Site with public profile pages
Yes craft provides many tools that allows public registration and editing the profiles without a single line of php or even a plugin. Most functions are covered by the cms and even custom functions like social media support is really easy since you can extend the UserController and change the things you need.

You have the ability to create dynamic user groups, give permissions to those and restrict content on the site via twig. Like with entries you can define a field layout for every user so you could create all the fields you can create in a normal entry and give users the ability to change them in a frontend form

You have config variables and settings that allows you to send custom invitation mails and validation mails.

But you need the commercial version for this. It's not provided in the free one.