>> This is no different from mathematics where each "X theory" is essentially its own language

Nice connection between models and languages.

The maths/physics discoveries achieved by using a new representation of a problem don't change the problem, they just present the issue at hand simply enough to be tractable. Each representation moves complexity trade-offs to a different category of problem.

I guess that does say something in favour of automatic syntax conversions but it seems too low level. Maybe conversions between the mode of abstraction being used is where it gets interesting.