I work in a museum, so I'll add in a couple of cents. Seth isn't entirely wrong here: museums are good opportunities for hands-on activities and to see things in a real sensory way that you can't in other places. "I believe museums exist to present the real thing for the visitor to experience with their own senses" rings really true to me.
That said: iPads and screens do have their place and it really depends on how well they're implemented.
First up: "But these physical exhibits require maintenance, and I was dismayed to see that several are in bad repair; some of them weren’t even working anymore, some seemed worn out, or didn’t seem well-designed to begin with."
This is probably the key reason why there are so many screens in this particular museum: he answers his own question. Physical items, especially things with motion, will degrade with time and use, and maintenance can get really expensive. Physical models like a human heart aren't something that you can generally buy off the rack: museums and similar institutions will work with a company to produce something like that (I'm guessing fiberglass?) These are things that can run thousands and thousands of dollars to repair or outright replace.
But here's the other thing with a physical static or interactive display: once they're in, they're in. You can't really update them without actually replacing the entire thing.
Here's an example: at the museum where I work, we have a section about the Civil War: it had some uniforms, weapons, and a whole bunch of other items that told the story as it related to our mission. The panel that outlined everything stretched across the room -- it was about 20 feet long. When we pulled everything out to update it, we had to replace that entire panel. It was a good fix, because the room hadn't been updated in like 15-20 years, but if we had wanted to pull out any one item, we'd still have to replace the entire panel. That sort of thing can be an impediment to updates, because it requires a lot of work. We ended up putting in three panels, which will allow us to switch out objects more easily.
We also put in an interactive with an iPad that allows visitors to explore a painting in the exhibit in a lot more depth.
We've done a handful of these sorts of interactives, and as I noted up above, the experience really depends on the audience and how well it's presented. In our case, we aim for ours to be usable for a wider range, which means that we have to keep things fairly simple, so adults and children can use them.
"My wife — a science writer who used to be the only staff writer covering space for New Scientist and before that, worked at NASA — poked at one of these with my son, added too many boosters to their launch vehicle, and were told it failed “for reasons” in a way she found totally unhelpful and pointless." That doesn't entirely surprise me, because she's an expert and is really knowledgeable in the field! But you have to make sure that you're calibrating for your audience: most of the people using that likely won't have her experience or knowledge, and digging deeper and deeper into detail might be lost on most of their audience. (Not having seen it, I can't tell for sure.) It is good to have that depth of knowledge be available, if you have audience members who do want to go further, but it could come down to limitations or be an exception that they didn't account for.
Digital interactives can also be swapped out quite a bit more quickly: if you have a new exhibit that you're putting in for a short amount of time, it might make more sense to have something that doesn't cost a lot if it's only going to run for months, rather than years. (Or if you find an error, there's new research, new updates, etc. -- a digital interface is easier to update than a static panel.)
On top of all that: cultural institutions are facing real crunches right now. There's a lot of uncertainty (and outright lack of support) from federal funding sources (which in turn impacts the willingness of private/state/NPO donors), and staff shortages that means everyone has fewer resources and fewer people to utilize them with. From where I sit, if we have to implement more digital content, we'll be able to repurpose the screens that we've already purchased to new exhibits and interactives.
Finally, there's nostalgia at play here: I have a ton of fond memories of visiting museums with interactives and huge displays, and I'm glad that I can take my kids to them as well. But I'm also happy to see that these museums aren't stuck in the past and the only thing that they're doing is rehabilitating old exhibits that are decades old or out of date: they still have some of those things, but they're also making sure to bring in new interactives, looking at new scholarship and best practices for museums (because museums aren't static organizations or fields!) to change as audiences change. Like it or not, there are a lot of people who use screens as a way to take in information: museums have to keep abreast of those trends, because if we don't deliver information to people in familiar and accessible ways, they probably won't come in.