"My hunch would be that the more specific and entrenched a genre is, the closer these bands stick to their styles (and lyrics)."
They usually also have the problem, that their fans often don't like them to change. They want more of what they know, but better. Not different (especially in entrenched genres).
Turisas for example, a band making songs mainly about vikings. I watched them live a few years ago - was quite good, but the band made remarks that they do not take the whole viking thing that serious (nostalgic buisness they called it) and would rather play something else. And they did one song in the end, in a quite different style (sounded like futuristic metal) but the audience was not thrilled - they were there for viking and glorious battle metal. So this is what Turisas are still playing, this is what brings them money, but they have not made a new album in over 10 years, but how can you make a good album, with a theme you don't find that exiting anymore?
If you want that, ideally you should spin up a new band name for a project thats too different in style from a band whose style you have already established.
Its not that people resist change, thats how thrash metal bands changed into death metal slowly and the invention of death metal is highly celebrated. But it was a slow and organic change. Typically bands that have some sense about this tend to spin up a different name if they want to play something totally different from their existing band.
In general, for sure. Only some big bands have managed to change their style and have their fans follow them. For most a different band would make the most sense. And I am only guessing about Turisas, but they probably should have done so, but it was probably more comfortable to make money with the established hits and name. Starting something new is not easy, after all.
If the musicians are already famous from one or other particular band, then they should easily pull up a strong fan following for their other projects too. Just look at how many people look up the large number of random projects of Speckmann even if say they had found out the band "Master" first.
They usually also have the problem, that their fans often don't like them to change. They want more of what they know, but better. Not different (especially in entrenched genres).
Turisas for example, a band making songs mainly about vikings. I watched them live a few years ago - was quite good, but the band made remarks that they do not take the whole viking thing that serious (nostalgic buisness they called it) and would rather play something else. And they did one song in the end, in a quite different style (sounded like futuristic metal) but the audience was not thrilled - they were there for viking and glorious battle metal. So this is what Turisas are still playing, this is what brings them money, but they have not made a new album in over 10 years, but how can you make a good album, with a theme you don't find that exiting anymore?