If you have another process for handling access requests in your organization such as a ticking system ( how much we love those, if I had a dollar for each ticket I handled   ….  sorry just imagining  myself under the palm trees zipping Pina Coladas). So, yes, if you have a ticking system, or even a SharePoint list with a workflow where you track requests, and you want to disable this feature, here is the long and tidies two steps:

  1. On the root site collection hit the site settings – > Permission.
  2. Select from the top navigation Access Request Setting and disable the check box Allow access requests.

AccessRequest