What would one use this for?
Transformer oil is typically quite thin (many transformers use natural circulation, many use forced, so viscosity isn't your friend here), very pure, and we do heaps of tests on them to ascertain how they are faring in their service life
Typical tests below.https://www.satcs.co.za/Transformer_Oil_Analysis.pdf
Some people dope them up as they get old, they can be put through purification plant (vacuum dehydration and fuller's Earth), some people just replace it (it's more predictable).
Have seen people use it as engine oil (stupidly, it's nothing like engine oil), and some use it instead for diesel fuel (*)...can go straight into the fuel oil storage tanks at the power station, which it can do if the recyclers aren't paying much.
(*) In the early days of dealing with PCBs, mildly contaminated transformer oil was recommended to run it through diesels...before thy worked out that they weren't hot enough.