That reaction makes sense, and it’s worth your athlete exploring - both whether they’re being treated differently (which would be an unpleasant feeling) or if the team happens to be comparatively underfunded. In my experience, the level of organization and early communication is usually about the program’s recruiting process (and its current distractions), which may or may not be reflective of the program as a whole. Some schools just send out itineraries closer to the visit, are dealing with details at the last minute, etc. I think it’s sort of equivalent to the level of organization at the admissions office: maybe it’s reflective of the school, maybe it’s not. Talking to athletes about how whether they have the resources and structure they need to be successful once they start is something your athlete should absolutely be doing.
Put more simply: maybe not paying for their visit is a sign; maybe it’s nothing at all. It really doesn’t matter if the school has a multi-billion-dollar endowment: the team has a budget and needs to make choices. It’s also possible that other prospective students told the school they couldn’t afford to travel on their own, or they make some decision based on geography, or a bunch of possibilities you can’t possibly know now. It’s information - useful but not determinative.
Hmmm. I have some thoughts here, take them as you wish. FWIW, I haven’t talked about it much here, but one of my children is a student/athlete who had a very similar profile.
First: your student hasn’t yet been accepted to this no-doubt-very-prestigious university, and so really has zero leverage. It is understandable to want to feel wanted (as @2plustrio said). Being #1/#2/whatever in a non-revenue sport is something the school values, and also they’ll be fine if your student doesn’t attend. Every coach I’ve ever spoken with has some story about an athlete they wanted before the visit and did not want after. Their job is still to be someone the team wants.
Second: this may be an opportunity to help your student get a sense of perspective. It’s amazing, and no doubt reflective of their very hard work, that they’ve built a set of skills that top universities choose to value, and so they’re willing to spend time and money to help your student see why whichever HYP this is would be a great fit for them. Also, there are tens of thousands of equally-amazing kids all across the country who will get absolutely zero 1-1 interaction from these schools whatsoever, will send their applications into a black hole, would no doubt be successful at those places, and will just get a “Sorry” note in their portal in the Spring. Your student is incredibly privileged to be in the position they’re in - even if some of that is their hard work, plenty of it is an unbelievable amount of luck - and I hope they can gain that perspective before they matriculate anywhere.
(Also, nobody is “captive” here, either practically or figuratively. C’mon.)