AFAIK, the Chrome Webstore only stores the latest version of an extension. It may be helpful to bring the Chrome Webstore folks into the discussion since most of the effort for such a feature would likely be on their side.

Version pinning of software can be quite dangerous from a security perspective. If an extension has a vulnerability and the author releases a fix, users pinning to an older version wouldn't be protected. 

IMHO if extension version pinning is implemented it'd be important to 
1. Notify an Admin/User that the pinned version is vulnerable
2. Automatically unload/block vulnerable pinned versions

Pinning provides the controls for enterprise customers and they knowingly know that the compromise is at the price of security for stability when they do.

I do like the idea of having the mechanism to alert both admin/user when a pinned version is vulnerable (having control over not alerting the user would likely be required by admins)

Perhaps this can be done with our enterprise reporting capability.  

 Issue 904849  has been merged into this issue.

I'll echo nrpeter@'s comment that we don't keep the old version in the store, which is problematic.

What would we do if a fresh install needs an older version?

I agree it would be difficult to backport this feature to extensions written with Manifest-v2, but the Chrome Web Store could keep multiple versions of extensions with Manifest-v3. This would give developers an incentive to move to v3 as well.

Just a FYI that Manifest v3 is public now: https://docs.google.com/document/d/1nPu6Wy4LWR66EFLeYInl3NzzhHzc-qnk4w4PX-0XMw8/edit#

We're now tracking this in the extensions product backlog as a possible feature to implement for manifest v3 extensions. We'll pick this bug up again in the future as manifest v3 implementation progresses.

I wanted to also add that with pinning, there is also a request to be able to rollback to an older extension.  This might be considered a separate FR.  But I wanted to also highlight this here.