Steve in the past!

The funny thing is that the Russos and the screenwriters each have differing explanations on what happened. The Russos said that Steve simply lived with Peggy in an alternate timeline, and then returned to the main timeline after Peggy died, while the screenwriters claim that it was part of a stable time loop, and that the old Steve Rogers had been living in the main MCU timeline all along, and simply kept himself a secret until that moment.

I much prefer the explanation from the Russos, but it doesn’t explain why Steve randomly appears on a bench, rather than teleporting back to the platform. 

The thing I take issue with is that it didn’t have to be like that. I don’t see why they couldn’t have just had an old Steve Rogers appear on the platform. They could do that and still make it emotional. 

My continuing belief is that Steve did stay in the original timeline, and as such he couldn’t alter anything significant. All that would do would cause another split timeline, not save anybody. Staying there wouldn’t be enough to shift the timeline, but major events like saving Bucky or correcting other terrible events would.

This is probably the best explanation, I think. It fits the rules and provides good explanation for why Steve didn’t change anything- If he did and it created a new timeline, then technically he wouldn’t really be changing anything because the “original” Bucky would remain unsaved in the original timeline. It would be no better than creating a fantasy world apart from the “real” timeline.

It still raises the question though of how he stayed so incognito. And even if he lived in Peggy’s basement for fifty years he still changed things because she obviously wouldn’t have gotten married her original husband, right? So that’s a pretty big butterfly effect right there. How did that not create a new timeline??

But... technically you can’t change the future at all even if you try, and if you do it creates a new timeline. And even buying a candy bar at 7/11 would have a potentially far reaching butterfly effect, let alone marrying someone who would have married someone else. The ramifications of that would certainly alter history even if it’s on a very small personal scale.
And how/why would the laws of physics(?) care/know the difference between small changes and history altering changes? Who/what judges such things? Different husband = no new timeline, but killing Thanos creates new timeline? That doesn’t really make sense.

In the end though, it’s really just impossible to write a time travel story without these paradoxes so I am perfectly fine with it not making total sense,

But do those small changes effect the present? That’s what I find confusing. 

Have you heard the theory that Peggy’s husband was always Cap, even before he traveled back? I like that one.

I have heard that one. The idea is that if the changes are small enough then they don’t effect the present, because they don’t effect how things ended up. So even if Peggy wasn’t married in an original timeline whether Steve is there or not, as long as she builds SHIELD then it all works out even. You need up seeing that she was always married to Steve because the events don’t force a new timeline.

With the time is a river idea it's basically how big the change impacts history, hence something like what Rhodey ate most likely had no real impact other than if he goes hmm, mmm mmm mmm or meh whilst munching on it, obviously this can differentiate between changes, like Rhodey could get sick from one bagel but not the other, and being sick can alter his day, maybe he doesn't meet Tony like he originally did, so their relationship never forms, and Rhodey does not become War Machine, or he could live out his life exactly the same except for the contents of his guts for a few hours, but it's based on I think the notion that time wants to happen a certain way, so it tries to course correct if anything changes, the idea with this though for the MCU means that when a change is too big however it creates a a new timeline which splits off from the main one, it a middle ground between the three typical ideas of time travel/timelines, where you have either a fixed, dynamic or multiversal timeline, where with the MCU you may have a dunamic fixed timeline within a multiverse, so time is malleable but wants to return to it's original shape, and if it can't it becomes it's own timeline.

Would this be the case in reality? most likely not, I think the prevailing ideas is either a fixed or multiverse timeline thing, where like they say in the movie, you cannot change your past as to do so causes you as you are to never exist then you get into paradoxes and closed loops, so either you can only go back in time to cause things that did happen to always have happened, or the moment you go back you most likely create a new timeline therefor any changes only impact that timeline, not your own, as such you can never cause yourself not to be born and shit, at worst all you do is prevent that timeline from having a you to begin with, but like I said I think the MCU has a hybrid of the 3 major theories of time travel, which basically means anything can go should the choose to dick about with time travel, which is better than having a set of rules you just break all the time like as is the case with the CW DC shows and their approach to time travel.

I prefer to think Steve didn't do anything too drastically. However, his presence in alternate 1949 would surely alternate the timeline one way or another. He would have had a hand in creating SHIELD for one thing. My only problem is that Sharon Carter would be creeped out and confused at how "recently revived" Steve looks exactly like her uncle did in his younger years.