Given various models, one that always produces statements that are false and another that only sometimes produces false statements, the latter model is preferable and the model which most people intend to use, hence the degree to which a model produces correct statements is absolutely a feature.
And yes, it's absolutely possible to systematically produce models that make fewer and fewer incorrect statements.
Sure, some may return results that are sometimes more true than others, but a broken clock is also right twice a day. The more broken clocks you have, the more chance there is that one of them is correct.
Infallibility is not a feature of any system that operates in the real world. You're arguing against a strawman.
How a product happens to currently be implemented using current machine learning techniques is not the same as the set of features that such a product offers and it's absolutely the case that actual researches in this field, those who are not quibbling on the Internet, do take this issue very seriously and devote a great deal of effort towards improving it because they actually care to implement possible solutions.
The feature set, what the product is intended to do based on the motivations of both those who created it and those who consume it, is a broader design/specification goal, independent of how it's technically built.
And yet they would both be operating within the normal design parameters, even the supposed "LLM that does not" when it spits out nonsense every so often.
Your current zeitgeist is not much better than a broken clock, and that is the reality many people are witnessing. Whether or not they care if they are being fed wrong information is a whole other story entirely.