G'day Luna,
I do think it's worth pointing out that literally every time I've mentioned dislike of infoboxes to non-WPians, the reply has been along the lines of "Why not? They're AWESOME!" I try to explain the objections, but usually the person is so set on the accessibility front that they can't see why anyone would want to avoid the boxes. It's not just bots that want information in an easily parsed format.
I think my perspective as (let's face it) an ex-Wikipedian is pretty similar to that of the common or garden-variety non-WP reader these days. (This may be why I've become significantly more of an inclusionist since I stopped creating --- and deleting --- articles). I tend to find the infoboxes alternately annoying and silly or practical and awesome, depending on my frame of mind and purpose. If I'm after specific information --- e.g. a recent case where a colleague and I were arguing over the population breakdown of the UK --- the infoboxes save me time and prevent confusion. If I'm just reading for the heck of it (cf. xkcd's "hours of fascinated clicking") they tend to be distracting. This is especially jarring in the case of subjects whose details don't break down easily into infoboxes, like real people.
As a reader, it's cool to quickly find the national motto of Burundi or the height of Centrepoint Tower without having to read through paragraphs of text. I love infoboxes! But also as a reader, it's distracting to have a professional wrestler's "coach" or actress's bust size floating in the corner of the screen. I hate infoboxes! I guess you can break that down to say: it's nice when there is a consensus view of what a given infobox should say; it's less nice when the people who populate the infoboxes have different interests and values from you.
Cheers,