Oil will catch dust like crazy and eventually evaporate or be absorbe; phosphoric acid is, well, an acid, I want none of any kind inside a transformer, even this "protective" kind, it will seep into laminations by capillarity and you will never ever remove it.
Mind you, I use phosphatization a lot: for my speaker frames and iron chassis (even aluminum ones) as a painting pre-treatment, but parts are later rinsed in distilled water (you would need to drop the transformer in a bucket of water to approach that) , oven dried and painted.
Varnish or plain synthetic oil paint works fine, in a "passive" way, just keeping oxygen and water away from iron but for better / more stable results use anti-rust paint (typically brick colour) which *actively* fights rust "walking under the paint" or for better finish, there´s a dual purpose top coat/rust protection paint available everywhere, won´t name brands because it´s Country specific, just ask the paint shop employee for it.
Here in Argentina we like:
"Triple action" here means:
* anti-oxide
* converter (similar to phosphatizing)
* nice shiny topcoat