This cultural expectation follows naturally from the nature of software. Software (especially of the networked variety) isn't something you can just deploy and be done. It has to be maintained to continue running over time as the ecosystem changes. The cost of this maintenance is lowest when amortized across the largest set of users, hence the success of open source software, and the desire to avoid forks. The people who are most qualified to maintain software are the original creators, so that is the path of least resistance.
Of course no one is obligated to maintain anything, open source maintainers abandon stuff all the time without any repercussions beyond passive internet rage.
Yep. The puppy analogy falls apart when you've given the same puppy to 10,000 people. All of them could pay the vet bill separately, but we instinctively recoil from that as being horribly inefficient (and personally inconvenient) when it's possible for just the one puppy-giver to pay it.
Of course no one is obligated to maintain anything, open source maintainers abandon stuff all the time without any repercussions beyond passive internet rage.