GitLab employee here. Just asked the Product Manager responsible. Project Access Tokens [0] will be available on Premium for GitLab.com and available on Free for self-hosted.
Certain features are disabled on GitLab.com in order to prevent abuse, are difficult to scale or just make no sense. In the case of the Project Access Tokens, the feature is quite new and it is to prevent abuse. See also the (nephew/niece?) comment I made in the thread (one to the side from yours, one down)
(I think Project Access Tokens create bot users under the hood that are associated with the token. So if one were to create hundreds of tokens that means hundreds of users.)
[0]: https://docs.gitlab.com/ee/user/project/settings/project_acc...