Indeed, Alfvén wrote that frozen-in magnetic fields in "plasma in interstellar space should be applied with some care":
Ref: Double layers and circuits in astrophysics, Alfven, Hannes, IEEE Transactions on Plasma Science (ISSN 0093-3813), vol. PS-14, Dec. 1986, p. 779-793 (also available online in full)
I thought that the frozen-in concept was very good from a pedagogical point of view, and indeed it became very popular. In reality, however, it was not a good pedagogical concept but a dangerous "pseudopedagogical concept." By "pseudopedagogical" I mean a concept which makes you believe that you understand a phenomenon whereas in reality you have drastically misunderstood it.
I never believed in it 100 percent myself. This is evident from the chapter on "magnetic storms and aurora" in the same monograph. I followed the Birkeland-Störmer general approach but in order to make that applicable to the motion of low-energy particles in what is now called the magnetosphere it was necessary to introduce an approximate treatment (the "guiding-center" method) of the motion of charged particles. (As I have pointed out in [5, sec. III.1], I still believe that this is a very good method for obtaining an approximate survey of many situations and that it is a pity that it is not more generally used.) The conductivity of a plasma in the magnetosphere was not relevant.
Some years later, criticism by Cowling made me realize that there was a serious difficulty here. According to Spitzer's formula for conductivity, the conductivity in the magnetosphere was very high. Hence the frozen-in concept should be applicable and the magnetic field lines connecting the auroral zone with the equatorial zone should be frozen-in. At that time (1950) we already knew enough to understand that a frozen-in treatment of the magnetosphere was absurd. But I did not understand why the frozen-in concept was not applicable. It gave me a headache for some years.
In 1963, Fälthammar and I published the second edition of Cosmical Electrodynamics
 together. He gave a much higher standard to the book and new results were introduced. One of them was that a non-isotropic plasma in a magnetic mirror field could produce a parallel electric field E|| . We analyzed the consequences of this in some detail, and demonstrated with a number of examples that in the presence of an E|| the frozen-in model broke down. On [12, p. 191] we wrote:
"In low density plasmas the concept of frozen-in lines of force is questionable. The concept of frozen-in lines of force may be useful in solar physics where we have to do with high- and medium-density plasmas, but may be grossly misleading if applied to the magnetosphere of the earth. To plasma in interstellar space it should be applied with some care."