I do think they should have had Coulson on board the Helicarrier since he was the one who had it commissioned to be rebuilt in the first place. Dude is pretty much walking around out in the open all over so I don't know how people like Hawkeye and Widow who still have SHIELD connections wouldn't have realized he was still alive by now.
Whedon said in an interview that this was done so that people who saw Avengers I but have not watched AoS would not be confused. That said, Coulson could have been there to hand over project Theta, and had a quick moment with the team with some quip about how they revived him.
I am surprised that I haven't heard any Whedon-hater complain that he put a character into the story that essentially looks at the audience and literally says "I bet you didn't see that coming" as he is killed off. LOL.