Not have a tree swing on an old tree and advertise it? The owner bares the burden of ensuring their service is safe - not the user. Try and imagine a world where that's the opposite as you're proposing.
This is not the brakes of your car services by some competent mechanic in which case I can easily see a liability issue but in the case of old stuff hanging from trees different rules apply.
For that matter, when visiting a friend who has two young children and a nice swing in their garden I spent the better part of a day re-inforcing the swing and its foundation because I thought the whole thing was an accident waiting to happen.
If you stay in someone else's apartment and it does not have a CO alarm and a stove that may or may not vent into the apartment then you should at a minimum sleep with a window open.
Tree-swings are not usually installed by licensed engineers, they are typically installed by people with a tree with a suitable profile, a rope and an old tire, any of which may fail at unpredictable times, but most likely when being used (and even more likely: when being used by an adult).
For all we know the owner of the swing tried it the day before but weighed 10 kg less than the guest and he/she never noticed a problem. For every tree-swing there is a point in its life where it will fail and a load that will cause it to fail right now.
In this case I'm not sure how anyone could defend the homeowner or AirBnB when the house had a picture of the swing on the website. Granted AirBnB isn't filtering those pictures looking for potential problems (hrm, image recognition problem here that could be interesting) but the owner sure could have if he/she were trained or asked to do so. Right now they aren't -- it is just a "host your home for free and get people to give you money" without thinking about the consequences.
I can see why the homeowner might not have all the insurance or knowledged needed to make it a safe(r) place. That's why they are homeowners and not hotel or apartment owners -- they aren't that sophisticated. But is it right for AirBnB to profit off of that?
I agree with everything else you're saying, but as for the example of states' rights vs. city rights, - while this may appear to be inconsistent, it isn't necessarily. It appears to be a contradiction if you interpret states' rights to be an affirmation of delegation to smaller forms of government on pure principle, but that's not what it is.
Advocates of states' rights base their argument on the Constitution, which specifically affords states (and the people) all rights that aren't provided to the federal government[0]. States reserve this power because the federal government actually draws its power from the states, not the other way around[1].
This isn't an argument that generalizes to the sub-state level, because incorporated cities and towns draw their authority from the state, just as the federal government draws its power from the federation of states that form the union.
You may or may not agree with the extension of this argument to advocate for the various things that states' rights advocates promote, but I'm just pointing out that this isn't actually a paradox.
[0] The tenth amendment is the most notable example of this, but there are other parts of the constitution in which states are treated as having far more sovereignty than any other subdivision of government: https://en.wikipedia.org/wiki/Tenth_Amendment_to_the_United_...
[1] Historically, this is obvious: the states had to ratify the Constitution before it ever even came into effect!