Any version? -Yes, any. Including the latest versions of React, TypeScript, etc. ? -Yes.
SharePoint Framework is supported not only by SharePoint Online but by on-premises SharePoint as well (2019 and 2016 with Feature Pack). SharePoint Framework Yeoman generator has different options for different SharePoint versions and it generates different project templates depending on the environment selection.
On-premises SharePoint is always behind SharePoint Online in terms of features and codebase. And the same issue applies to SharePoint Framework. If you generate a "Hello world" SharePoint Framework web part for SharePoint 2019, you will see that it uses React 15.6, TypeScript 2.4 and Office UI Fabric React (OUIFR) 5.21. The most recent versions (as of today, August 2019) are React 16.8.6, TypeScript 3.5.3 and OUIFR 7.21.0.
Now you see the issue - you always have to work with an older version of packages. You miss a lot of potential features, bug fixes, and other things. Additionally, from a developer perspective, it's not exciting to work with outdated technologies or frameworks. The situation will be even worse in 2020 when we see React 17, TypeScript 4 and OUIFR 8. Will Microsoft update yeoman generator for on-premises to add support to the most recent version of packages? I don't think so. On-premises are not in the priority list today.
For those who want to jump and explore the code right away - the full source code for this post is here at GitHub. More...