I can only really speak to astronomy, but the biggest problem is generally not hosting the raw data. The problem is maintaining the process of analyzing the data.
When you are doing science, you often do not just have a single standardized data format. It's not like taking a picture with a camera, where the jpg format is a standard and the metadata is a standard. If you are, say, storing data from a radio telescope, the metadata is more like taking a snapshots of a production database. Over time you might track additional data, like how much the telescope slewed recently, how much radio interference was nearby according to some new algorithm, etc etc.
Your data formats are constantly changing. So your analysis scripts are constantly changing as well. But this sort of thing doesn't just maintain itself. You very often need to add code like, how do you handle versions of the data where column X is missing. A research project might spend a year gathering data, and change the data format a tiny bit ten times over that year. If you publish something a few times a year, there eventually are a huge number of data versions and script versions that old publications rely on.
It isn't impossible to maintain data like this. You can have code that regularly runs integration tests and reruns past analyses. But most research doesn't operate to this level of "software engineering quality". One-off Jupyter notebooks, code that the developer only got working on their local machine, and so on.
I think we could do better, but it would involve hiring more software engineers and building engineering teams to support scientific research. It is not as simple as allocating more budget towards hosting large files.