It's hard to get meaningful answers to these really general properties you're after:
> communicate well
This has so many elements and is really only fully visible after you work with someone for a while. Sure you'll catch some red flag issues, but such issues likely to be caught are also likely to be caught no matter what you're talking about, so this can't be the primary purpose of the screen.
> motivations for looking for work
Is not wanting to trade services in exchange for money in a valued environment enough? But sure, aspects of this for most people can be an important subgoal, it's just important to set expectations on how easy it is to game and how unreliable the signals will be. I've sometimes found it useful to probe seriousness and a sense of longevity commitment (if that matters, and can be incentivized without needing to probe), and some of their values, and whether their idea of your actual environment matches your reality and how much that matters (the candidate should be actively participating in this with their own questions though), but again reliable signals are hard. Once I helped screen a manager who was thinking of coming back (he had previously left a couple years prior) to the company to manage a new project, and got out of him when asking what might stop him from leaving again in a year the vague (if true and agreeable) "you never know what opportunities life will bring" and concluded he wasn't that committed for the role I felt needed someone willing to put at least a few years at it. It surprised another guy who talked to him, but he hadn't probed into that.
> logistical
Seems this could be handled before any conversation takes place by clear communication about whether the role is remote or not, how much office time is required, whether relocation support is offered, and so on.
> compensation
Also can be handled before any conversation by having salary ranges for the role. If they're too low, a good candidate might go through with things anyway and try to negotiate beyond the range.
> getting all the deal-killers out of the way is the point of the phone screen
Ultimately I agree with you on this, but I think the biggest deal-killer for a technical role is: the candidate cannot actually program at a level you require. I'm a fan of Yegge's process (https://sites.google.com/site/steveyegge2/five-essential-pho...) and warnings and have used my own variant for what we cared about more, but frankly if your screening doesn't require some level of coding at least on the level of fizzbuzz or easier (but adjust to requirements/expectations), sooner or later you're going to bring someone in for a full round and discover they can't program, wasting possibly considerable time (more than five hours when adding it up for everyone involved) as well as the opportunity cost.