That explanation would still have to mean that the Falcon and friends we see in the parkbench scene must have lived their lives in the timeline where Cap has been with Peggy all these years.
Yes
and no. Falcon and friends have lived their lives in a timeline where they don't yet know about Old Cap because that hasn't happened for them yet. They've been hanging out with Young Cap as depicted in all of the movies.
So it is not the same timeline we saw up to that point in all the MCU movies, but the dudes still seem surprised him popping up as an old guy. It does not compute.
Ignoring sci-fi nonsense, the accepted theories on time concur that it is
relative, and this is clarified in Endgame. There are at least two timelines at play here which are, seemingly, mostly the same anyway. Given this, why
wouldn't Falcon be surprised to see Old Steve? They could not possibly have known about him until his appearance.
From Steve's perspective, his life chronology (ages 1 to 105) was being born in 1918 then becoming Captain America in 1941 (age 23), where he fought the nazis until 1945 when he was frozen in ice (age 27). He was thawed out in 2011 (still age 27ish), rejoins SHIELD and engages in many Avengers hijinks until 2023 and the events of Endgame (age approx 39). He then goes back in time to 1945 to live with Agent Carter and lives until at least 2023 (Endgame) where he would be 105 years old if Old Cap wasn't snapped, and 100 years old if he was.
Until Endgame, at no point during any of the previous MCU films, would Steve have known about being with Agenct Carter because that was in his future, even if the events took place in Earth's linear time history.
As to why Steve may have lived a quiet life, I think there are a few sound reasons. First, Time Travelling Steve (age 39+) knows all about SHIELD, Hydra and other organisations that might pose a problem for him and Carter. More importantly, although all of the events depicted in the films in his past, they are yet to play out in the timelines he's now in. Frozen Cap still needs to be discovered, recovered, build the Avengers and save Earth and the universe a few times. There is a fascinating risk/reward dilemma of could Time Travelling 1945 Steve saved a lot of suffering and death if he tries to pre-emptive and prevent the events in his past, that have not yet begun to playout in his present.
I guess I have a problem with their basic premise that they're actually time travelling. They're not, they're dimension hopping to parallel universes to get the new infinity stones and in the end Cap will be returning the stones to their original universes. He wouldn't actually be in the past of their timeline.
I think it depends who's language who wish to lean on. Ant-Man says it's time travelling, so does Tony Stark and Bruce Banner. The Ancient One at the New York Sanctum, where Hulk retrieves the time stone, also confirms these are different
timelines. Maybe somebody use the word dimension, I honestly can't remember, but the phrases "time travel" and "time heist" were used a lot.