Auto Add Recordings to Original Meeting Invite

Is there a way to automate the process to add a cloud recording link back to the original zoom invitation?

My organization uses Google Calendar and we have the Zoom Plug into schedule meetings. When integrated into the Zoom platform (on Mac), it will show my upcoming meeting schedule where I can quickly Join or Start a Call. I occasionally record a meeting to the cloud. Then I have to wait for processing and Zoom auto-sends me an email. Assuming I am sharing that meeting back to the original list of attendees, why can Zoom not edit that invite with the recording and re-send it to everyone who was invited to the meeting?

There would need to be controls around this and an ability to have the system to NOT do this when specified. 99% of the time though, a feature like this would be handy for my meetings or meetings I am a part of. 

There is a lot of leg work finding a recording for a meeting. There should be an automated way to share these within calendar integrations.