> that there is no objective question about preferences that they ask
I don't see this as an issue. I also don't see it as a problem to specifically non-ordinal, but to every system. I like to try to explain a STAR05 ballot simply to people with a forum they are very familiar with. A ballot might look like below
How do you feel about ___x___ candidate?
Very Unfavorably, unfavorably, neutral, favorably, very favorably
Those are your 5 options. Yes, this isn't exact, but we can't have an infinite score. But as we understand distributions, we know that the fluctuations won't matter much. If a group of people have an "honest" opinion that a candidate is rated "favorably" (or a 4) we'll see a distribution around this (a fairly tight distribution). So you'll get some 3's and 5's, but most people will give 4's and the average will be 4. So it isn't an issue. Similarly, if you are ranking people and view two candidates equally 50% of people will put candidate A in front of B and vise versa (well real world there'd be a bias for things like: who is listed first, "nicer" sounding name, familiarity, etc. But still, that's not too big of an issue because at the end we get pretty close to the optimal efficiency that the system can provide). You have to remember that there is no perfect system, Arrow and Gibbard showed that. But the question is if we statistically come close to the optimal (that the system can provide).
I want to point out that simple approval voting is VERY effective, even though it is low precision. You're literally choosing "like" and "dislike." Analysts aren't that concerned with the lack of objectivity in the difference between a 4 and 5 or a 3 and 4 because it is much more refined. If this is a major concern, then extend the expressiveness by increasing the range, e.g. 0-10.
I would also encourage you to listen to that interview that I linked. Arrow briefly discusses this topic. He makes some criticisms of score voting but also says it is the option he would push (question is which he'd advocate for). Remember, there is no such thing as a perfect voting system. There's always a trade-off. We're just trying to minimize the trade-offs.
And personally, if someone made RP popular I would gladly advocate for it. But because we're trying to trade one shitty system (plurality) for something only slightly less shitty (IRV) I am going to be vocal about the issues and lying that is happening. I don't really have an issue with RCVs, but specifically IRV. This is why I wanted to make a clear distinction between the two. Because when the discussions come up we end up using different languages, using the same words to describe different things. This may have been a smart move by Fair Vote, but we're on Hacker News and there's an expectation of more nuance than we'd have in other places like Reddit or in person.
There are conditions which resolve this (e.g., when ballot markings in a method like score voting represent the amount of some valuable resource the voter commits to paying if the given choice is elected, or where markings in approval represent a binding commitment to not participate if an non-approved option is chosen and/or to participate if an approved options is chosen.) But these resolutions are typically not available or desirable in most public elections.