Here is some context.
I think it is safe to say, in any bargaining situation we should have symmetry – I cannot fathom how to resolve a dispute over "who is player 1" in real life, or how to even process the question (Rubenstein has an answer, sort of – whoever makes an offer first – but real life is full of RFPs and I'm not sure we should trust in the hyper-specific details of a model where first offers have an advantage, when in reality businesses deliberately choose to be second).
Pareto optimal solutions seem good – or rather, all non-Pareto optimal bargains are (by definition) replaceable with a weakly better bargain, and I think it's relatively uncontroversial to suggest we ought to do that (although, hearing some of the discussion about how random people being billionaires somehow hurts people regardless of what that mechanism might be, perhaps this claim is less popular now than it was in saner times).
And don't even get me started on solutions being invariant to affine transformations. I've been saying for months that this is necessary, in casual conversations, to people who might understand. Utility functions are only well defined up to affine transformation! The numbers are all made up! It would be better if there was some mathematical object (like a Minimally Ordered Field, that'd be a good name) that made this more explicit. Then we wouldn't have to even use numbers, hopefully, we'd know to express values as multiples of [base, unit] pairs. This is a somewhat esoteric point but suffice it to say I believe it is an error to skip over this requirement.
But the major alternative to Kalai-Smorodinsky bargaining solutions is the Nash bargaining solution, so it's worth talking about their differences, not just their similarities.
Fundamentally, I'm interested in one empirical point and one theoretic point. Empirically, we see that we do not have independence of irrelevant alternatives. People avoid voting third party when someone they super disagree with is on the ballot. Obviously this is a consequence of the structure of the voting process, but still, we observe real life decisions do not let people actually have this common-sense property, and (while I disagree with tactical voting as a practical matter), I am not entirely certain they're wrong to avoid it.
But more fundamentally, without the resource monotonicity axiom, we are no longer incentive compatible with utility maximization. There's an extent to which, if you could benefit from the system having fewer resources, whatever Pareto optimality you might observe is unstable. It exists only so long as there is no way to destroy, waste, lose track of, or fail to find or produce the resource. I can think of no actual resource for which all of those are impossible, although I admit there might be one in theory.
The most interesting part of these models is that they actually let people prove things based on their presumptions. Bargaining solutions are interesting because they correctly observe (as unfair as it may be) that the world exists with a status quo, and there's nothing in principle forcing agreements to be made.
This is one of those weird things where I might actually use this to produce actual business proposals, too (albeit with estimates of marginal gain for both sides).