Why does "Cancel People Account" not work?
I can confirm your suggestion what it actually should be like and that actually exactly that should happen what you expect. After canceling an account you will be provided with further steps about the users written content etc. and finally you will become a progress bar showing the deletion or re-assigning of the written content of this user and the final confirmation about the success of it all.

The misbehaviour what you describe can be caused by several issues I only can list here for your research: 


there is a mod_rewrite issue sometimes if the server is not set up correctly but this would actually also come up by many other tasks
is your admin account clean and has never been modified? The user 0 is something special in Drupal world and can sometimes be corrupted by some changes on it
you mentioned a local installation. Does has your DB user which is connected to the DB management of your Drupal installation, the right to DELETE in the mysql database?
and as mentioned by Molot also the redirecting via overlay or any other modal frameworks and jquery can be the issue, often fixed by using jquery_update module and playing around with jquery versions in the settings of the module.
Also, any PHP cache or similar can cause freezing batch processes or overwrite the use of pecl progressbar (default in Drupal)
Did you tried different users or only one? Or is this user you try to delete a spam account? They also can cause issues since they are not really registered but somehow signed up. This would be another story ...


Sorry, just some ideas...