It goes without saying that 'Avengers: Endgame' was going to be just that - the end.
The question was always for who was it going to be the end. Chris Evans and Robert Downey Jr. were both the most visible and recognisable characters in the Marvel Cinematic Universe. Both Iron Man and Captain America made up the heart and the brain of the Avengers, so now that their work is complete, that's it for them.
But wait, you're probably thinking, maybe not? After all, we just sat through three hours of people trying to undo the past to save the future. It could work that they maybe can be brought back, no? Absolutely not. The manner in which both these characters were sent out on the screen would not only negate the whole reason for that ending, it just wouldn't make any sense. Plus, nobody can afford to pay Robert Downey Jr. anymore and Chris Evans clearly wants to make touching indie dramas.
More than those cynical, careerist reasons, these characters have had the full arc. From 'Captain America: The First Avenger' right through to 'Avengers: Endgame', the whole arc of the character has been about how Steve Rogers sacrificed his own happiness - personified by Peggy Carter - for what needed to be done. He went into the ice, knowing he wouldn't come out. When he got out, Peggy Carter had moved on and was an elderly woman who had lived a full life without him.
When he manages to finagle the timeline so that he saved himself from going into the ice - and then went back to her - he got everything he wanted. He had done his duty, and he managed to enjoy a peaceful life with the woman he loved. You'd probably need some kind of map to figure out how he did it, but nevertheless, seeing an elderly Steve Rogers hand over his shield to Sam Wilson was the graceful exit the character deserved.
You could argue Tony Stark made the bigger sacrifice. After all, Tony Stark got lucky with his life post-Snap and raised a daughter with Pepper Potts. It's one to sacrifice when you don't know what you're giving up, but it's another thing to do it with the full knowledge of what you're leaving behind. For a character who began life on screen as a self-centered, egotistical billionaire with no concerns beyond himself, it's the complete arc.
Was it a tad overwrought? Definitely. You could definitely sense a certain amount of 'Lord of the Rings: Return of the King' vibes off of it, and the scene in which all the remaining Avengers return to see him off felt just a tad bit overdone. But, then again, we could hear a number of people sniffling at the press screening - so who's to say it wasn't the same when you went to see it?
Also, no need to stay in your seats - there's no post-credits scene.