no i think you’ve got it wrong. Instead once he decided to stay there would’ve been a point in time where there would’ve been two Steve Rogers for decades. And I don’t buy that he wouldn’t have informed SHIELD of Hydra’s infiltration. Which means a LOT of the future would change. When they said “the future doesn’t change” I was like WHAT?!? That’s not even possible. I mean, we saw when Steve decided to stay it obviously changed his girlfriend’s future.
I guess it all depends what part in time he decided to stay in. Was it after he was lost in the ice and he just lived that part in time, then the other Cap was found and thawed out and now you have 2 Caps, one young and the other old? Like I said, when movies use time travel, they never seem to get it right or just make it up to fit the narrative.