Peacock has always had issues with live streaming sports, so this doesn't surprise me. I know soccer had similar issues. For the longest time WWE PLEs were like how you described.

If you missed out on the start you couldn't start from the beginning. You had to join live and wait for the event to finish to catch up on what you missed. They eventually fixed it.

So I don't think it was licensing issues. Peacock just sucks when it comes to live event playback.