That approximation, called “magnetohydrodynamics” or MHD, was invented by plasma physics pioneer Hannes Alfven, who won the Physics Nobel Prize in 1970 for his work. Alfven repeatedly warned astrophysicists that the approximation was only valid in certain conditions, with dense plasma like those in the sun.
When his warnings were not heeded, he repeated them strongly in his Nobel address (https://www.nobelprize.org/prizes/physics/1970/alfven/lecture/), (a clear, non-technical presentation), saying that many basic concepts used by astrophysicists “are not applicable to the conditions prevailing in the cosmos…it is only the plasma itself that does not ‘understand’ how beautiful the theories are and absolutely refuses to obey them.” (See p. 3-4 of PDF, with a simple table comparing wrong and right approaches.)
For a fuller and more technical discussion, see p.15-17 of Alfven’s 1986 paper (http://www.diva-portal.org/smash/get/diva2%3A514247/FULLTEXT01.pdf). MHD theory can’t explain the focused beams of energy that emerge from compact objects such as quasars and Herbig-Haro objects, which are ordinary stars in the early stages of formation. These beams are routinely observed produced by plasmoids in our laboratory experiments, explained by correct plasma theory.