How do you handle Groups / SharePoint / Teams creation

End users cannot create SharePoint sites or sub-sites in both our on-prem and early O365 environment. We have a 'SharePoint Request' list form that users must complete to request a new site. We will do the same for O365 Groups (or merge the two as the same request) for O365. For on-prem, once the user submits the request I get notified and use a PS script to create the new site; for O365, we may use the script or just create them manually.

The point is control - but not too much. For example, Site Owners are largely responsible for setting up libraries and lists, and modifying pages as required.

We've had SharePoint running since early 2012 (2010 upgraded to 2013 two and a half years ago). In that time, we've created just on 245 sites collections, of which 94 are team sites (with 425 sub-sites) and 83 project sites (with 85 subsites). Note, we have different web applications for on-prem team and project sites, but they use the same template. We have around 8,000 staff across a widely dispered geographical area (State) in Australia.

Our current project sites will become Group-based sites, while the team sites will be a mixture of Group-based and SharePoint Admin-created.