we don’t know of any insurance like the one you suggest… and we have asked several insurance companies.
I am also not sure about their reasons…
I believe checking the financial health of the school you want to sign up with would be a wise move.
We had one student that told us our financial situation was one of the reasons why she joined us… but it has been the only one that mentioned it.
in the UK, you can check Companies House for most of companies. In other countries, you may need to pay something to get that type of information (I would say between 30 an 60€ so nothing crazy)
Summarizing… your point is very interesting and should be considered more widely by more students