Your problem isn't that they didn't invite them, rather that there was no scene of them really bonding or kind of reflecting on everything as a group. So it felt like a big disconnect. They already had been apart for most of the books. So the ending with Asami being with Korra on their own, and never with all of the group, kind of solidified that the group really...wasn't friends anymore.
That is the perception you get. Since the ending only has characters off on their own. And it also gave no time or conclusion to Mako or Bolin who were supposedly pivotal members of team avatar (they got more screen time then Asami). Kind of funny, because when all is said and done, Mako and Bolin DID do more for Korra then Asami ever did. Just in terms of what they did during major battles. And yet they never got to reflect or be in any kind of conclusion of this journey Korra was on. They were just left to the side (cold).
They pretty much lay down their life for this person, that can't even bothered to give them a time of day. Pretty terrible stuff. So it makes Mako's loyal to the end line even more cringe in hindsight. Oh thank you Mako, that's nice to know you will die for me. Excuse me, going to go be with Asami now.
Also Asami not interacting with Bolin or Mako all Book 4, also made it seem like she was no longer friends with them. The whole "group" thing was actually kind of depressing when you think about it. Granted, the writing was always bad for the group. But in Book 4 you get a sense that, the group has drifted apart, and their friendship isn't really there (which logically, I guess none of them being friends including Asami and Korra never entirely made sense).