The answer is simply: generally they are not frozen-in.
This is mainstream understanding.
However, the frozen-in conditions are often met in practice, at least approximatively.
There is a marked difference between a guy who is trying to simplify some equations while he's working on a tokamak reactor, and an Astrophysicist or Astronomer who is trying to analyze an observed phenomena in deep space and trying to understand what they are looking at! Astrophysicists and Astronomers are observational scientists- their job is to report what they preceive at the farthest reaches of Mankind's vision, and report it as accurately and precisely as possible. They have no business using shortcuts like 'assuming infinite conductivity/frozen EM field in a given reference frame' than they have to round up to the nearest whole number!
Maybe you missed my point- I'll admit that I didn't specify whom the subject of my focus was:
'Astrophysicists, Astronomers, and anyone who works with them in trying to understand the specifics of the physical phenomena we witness in the Universe around us.'
I thought it was pretty apparent that most of the topics found on this board are pretty much aimed towards the competing cosmologies- the Mainstream vs. IEEE's Plasma Cosmology, and it's off-shoot the Electric Universe.
It was a bit insecure of you to presume I was chastising engineers for making a mathematical shortcut in an equation to simplify a parameter in an experiment, I think.
Last but not least- I wouldn't give too much credit to those Astro guys when it comes to understanding plasma physics- we can cite *numerous* examples of them stating things like: permanently frozen-in magnetic fields (that were generating current!), open-ended magnetic lines of force, lines of force twisting/snapping/breaking/reconnecting, etc.
No hard feelings tho, bud! I'm built tough enough that a few cracks against my 'though processes' don't really bother me- I'm pretty proud of what little I have learned so far, and with no professional education in the subject as a basis for it!