1) Bitcoin as it is running right now with no significant development team to love it at first
Will you explain why you think 1 will happen? I am non-plussed
Love that word "nonplussed".
I can't remember exactly where (somewhere in this forum for sure; getting too old) but I saw something about neither SW nor BU gaining enough "votes" and so Bitcoin would just plod along as it is (I could easily have misunderstood). From there I speculated that neither camp would be content and so they would both hard fork into new altcoins.
It probably isn't safe/reasonable for me to speculated thusly; it's kinda like letting kids play with matches.
Why does Core automatically get to keep the legacy? Why does BU have to fork off?
Ok, I think I see what's leading you to say this.
To begin with, remember that BU is explictly defined as a hard fork. Naming no names, but there are some excessively over-complicated descriptions of the difference between the two. But there are nuanced sub-categories of each type, so there is some grounding in reality to presenting every subcategory at once (but it's more confusing presented that way).
It's clearer like this:
The 2 overall categories: hard and soft
Hard fork: the blockchain splits in 2 1 Rule or more are either changed, or removed. The implications are that those running the previous versions of the Bitcoin software detect the new and different version, but refuse to accept the new version of the blockchain, because the new blocks allow actions that were not in the previously rules. That's why it's described as "hard", it's an all or nothing change, as a user, you're forced to choose one or the other, because you cannot choose both.
Soft fork: the blockchain remains as 1 All the previous rules are maintained and respected by the newer Bitcoin software. The difference is that
extra rules (that don't contradict the old in any way) are added to the new software. Bitcoin was designed specifically to let this happen smoothly, so that when previous versions encounter blocks that observe new rules they do not have the code with which to understand or apply, there is a predefined way for those older version of Bitcoin to safely ignore the new rules (how could the old software interpret newer code that was written in the future?). So, the implications here are the opposite to hard forks: people running the old version don't have to choose between 2 blockchains, they can stay on the same chain as the newer Bitcoin software, ignoring the new rules while still observing the old rules.
With that out of the way, it should be clearer why it's not that likely that the 3 chain forks you suggested would happen, or, at least the way things are now. For your scenario to happen, either Bitcoin "As is" must do a hard fork from Bitcoin "Segwit", or the other way round. Because there is no proposal like that right now (or at least not with any meaningful support), it's far more likely that only one out of 1) and 2) would take place, not both.
And your final question, I hope, should be inherently easy to answer for yourself now: because BU makes changes to pre-existing rules, it is a hard fork by definition. BU must fork into a separate change to allow BU's changes to be expressed in blocks, because older nodes will reject BU blocks as they break the previous rules in Bitcoin.