There has been much discussion which I won't repeat.  Many commented that, for certain users, getting them to click a link in an email is a challenge (and I understand that).
I have 2 suggestions:

1. Provide a means for owner/mods to resend the "re-subscribe" email with the link:
   1. with updated easier to understand language and terminology
   2. allow a customizable section for a personalized message
   3. the From: address is the owner/mod, not the group address
2. Provide a means to send a "re-subscribe" email - but this email does not contain a link:
   1. allow a customizable section for a personalized message
   2. the From: address is the owner/mod, not the group address
   3. the Reply-to: address is set to a special address which will resubscribe the member without further ado (perhaps GROUPNAME+resubscribe@groups.io).

Suggestion 1 has been mentioned elsewhere along with extending the time period for the Re-sub link.
Suggestion 2 does not require the member to go to any web page, they stay in their email.  They only need to click Reply and Send.  I would suggest that the resubscribe command email does not generate the welcome message or an email containing a link to confirm - if the sender was previously subscribed to the group.  This would require groups.io to retain knowledge that the member was unsubscribed from the group, essentially in suspended state as has also been suggested.

Thanks
Toby