Stubborn Insistence, huh? Sorta like how you've spent about 15 of these 31 pages telling us the lifeboat couldn't possibly be capable of independent travel, and that some of this only made sense if it was a tethering-type situation? Or you getting hung up on genetics when no one was arguing it, and then later trying to bash us over the head with the point we were TRYING to make at the time? You crack me up sometimes.
BTTF is a great example. When Biff messed with the past, and then Marty went forward in time in BTTF 2, things were a tad different, weren't they? If Marty was having a conversation with car wax Biff before he left (or his mother, or the principal, or...), can't pop back to 1985 and finish it. Even when Marty 'fixed' everything in the first movie so that things were basically the same, they weren't the exact same, and if Marty was talking with his parents at the start of the movie, he's not continuing it later. For things to make sense, more changes like at the end of BTTF ought to be happening regularly. Most everyone's still there, but minute differences, maybe someone random is there or someone is missing occasionally, etc.
I understand that it's tough to maintain a series if the characters don't retain anything week to week, but they need to work with the premise to allow it somehow, or maintain that things are happening similarly, but not always exactly the same. Some sort of bubble around the facility would allow for most of that, but it's never come up.
With that in mind, when Rufus and Wyatt stole the lifeboat to save his wife, they left Lucy behind. Wyatt asked Lucy the outcome right when he got back, and she was able (if i'm remembering correctly) to tell him that he saved the other two, but his wife still died. How would she know about the other two women? They just returned to a timeline where they never died, and wouldn't be part of the history where his wife died.
Unless something even crazier is going on, and you displace your 'current universe' counterpart when you show up, but don't get affected by other changes somehow? The team is from history 1 (well, 2 really, but whatever). They left Lucy 1 behind in history 2, but she remembers history 1 only. They change the 80s, return to history 3, but somehow Lucy 1 is still there? Where did Lucy 3 go?
The show very much needs shielding or a protective bubble or something to explain why the support crew isn't affected at all by this. Although they remember the Bond movie and whatnot, so sometimes they ARE affected. Ugh....
I'm really not convinced that the writers sat down and came up with many, if any, rules for how this works. I get that concessions need to be made, but it really ought to be somewhat consistent and make sense in-universe at least. This is all just random and week to week, and ignored completely when they feel like it. Very frustrating, no internal logic. Easier to accept a silly premise or rules if they stick to them and they make sense. When they slap it together (like the lifeboat being able to travel independently ought to let them end the show in the first episode or two, instead they're intentionally showing up at bad times?), it's tough to take seriously.
To bring it around to Star Trek, take The Enemy Within. Real answer is that they hadn't thought of the shuttles yet (or budgeted to show them, or whatever), but they were trapped on the planet because they couldn't use the transporter. No dialog about why they didn't just fly down and grab them instead. It was early, we forgive them, etc. but not the sort of thing you can keep doing over and over again and have it make any sense. I'm going to just pretend that something made it unsafe to fly and no one mentioned it on screen, but hey, retcons are wonderful. In Timeless, though, they already had the equipment and a reason to use it, and just don't. Over and over again. Why?