We open the film with Kirk in command, we end the film with Kirk in command. Consequences are usually things that stick for the long haul and affect things move forward. The consequences of Star Trek Into Darkness are so minuscule that you could skip over 'Into Darkness' entirely and go straight into 'Beyond' without missing anything.That actions have consequences.
You can't go from Star Trek: The Motion Picture into Star Trek III without missing a TON of important moments, just as you can't go from Star Trek II into Star Trek IV without missing all the important moments (Well, unless you watch the UK version). There is nothing that happens in Into Darkness of importance that audiences would need to know in order to better understand Beyond.