The idea that sons before daughters is some uniquely Andal idea is ridiculous - the North does the same thing and it was Aegon, not Visenya, who inherited Dragonstone.
The North isn't Valyrian, either, and as for Targaryens, once again, the whole issue is that there is no such thing as a codified Targaryen succession law like there is for Andals or Rhoynar. Which means one cannot call upon succession law to invalidate a chosen heir, because that law doesn't exist.
But again, I think we should assume that the canon characters had at least competent advisors on this, and if it was that important that they fight under the red and black they would have done so.
If we employ that logic across the board, then the whole quest becomes kinda meaningless. The entire point is that here we can make our own decisions and employ our own strategies. And while the colours and arms may not mean much, it is also no great cost. It costs us literally nothing not to modify our arms - but if we discuss what our arms should be,
which we had, then legitimacy is a valid argument in favour of not modifying them.
As I have said, let the traitors modify
their arms if they so wish, we are the true Targaryen line of succession, and nothing else. We are not just one war side among many, as good as the others. And we should act accordingly, and not preemptively weaken our legitimacy - regardless of how little that means, because it's not like we gain
anything from modifying our arms.
It's a recurring GRRM point that legitimacy is a shadow on the wall, and the only King the smallfolk really care about is King Bread.
Yeah, but the smallfolk don't matter, and you see legitimacy
repeatedly being a thing among the nobility, actually. Why are there still Stark loyalists in the North even after the House is considered to be all but extinct? See Manderly's speech - "the North remembers". Hell, the entire reason the Boltons even do their whole fake "Arya Stark" charade is for the sake of legitimacy. And you have that in several other instances as well - Lancel's marriage to Ami Frey was because she had a Darry mother, so in order to secure Lancel's hold on Darry. Other marriage plans follow similar considerations, all about gaining legitimacy for newly acquired lands. Because legitimacy actually
does matter, and that a great deal. There is a great deal of legitimism and loyalism, actually, like the actions of the Darrys in smuggling out the Mad King's youngest children, or the unshaken loyalty of the Dornish nobility to the Martells during the Dornish Wars - even as all their holds were burnt down but Sunspear spared, even as they all had to flee into t he desert, even as the Targaryens put huge bounties on Martell heads.
And even in mattes of Targaryen succession - yeah, sure, political factors were a big concern in how successors were chosen in Grand Councils (because, again, there is no codified law of succession for Targaryens), but matters of legitimate descent and all that mattered as well. We should not think that this is not a factor at all in succession disputes, it very much is. After all, the whole system of nobility
rests on the notion of legitimate succession, even if the rules are not uniform.
And in terms of book themes, I would actually say the opposite. Power rests where people believe it to rest. Varys' assertion is seen again and again and again in the books.
That is a theme of the books. Yes, you can describe that as "power is a mummer's play", but I think the reverse is much truer - power is
upheld through a mummer's play. Legitimacy is what leads everyone to believe they should follow this or that guy.
Plus if nothing else, I just don't see a reason why we should lessen ourselves and not claim full legitimacy in our actions, insignia, symbols, etc? Why pre-emptively give up any of that.