Most extensions already have the ability to update themselves with update_urls and manifests. I don't think it makes sense to reinvent that.
I think the primary thing that needs to be addressed here is local file updates (which I'm solving). And I'm adding in the URL comparison to help in other situations.
If you are serving a custom extension via https, you should have an update URL in that extension and you should have an update manifest and that's how the extension should get updated.
I can't download the extension from the web at every startup and check if there is a new version - that's just not feasible. I could download an update manifest, but that assumes the extension already has one. which means there's no need for me to download it, just allow the extension to update itself.
Chrome solves this by having the install link for the extension be the update manifest, not the actual extension. I'll investigate doing that in the future, but it would still involving basically having an update manifest somewhere.