I can see why PH and ST would be considered pointless. The games may have added new aspects to the series, continuing the new 'tri' tradition... but this came at the expense of what a lot of the older games -- and if I'm not mistaken the very reason for the spirit-princess-evil repetition -- built upon as staples of the Franchise. We lost Ganon. We lost the Triforce. We lost the Master Sword. Heck we'd already lost Hyrule and I still hesitate to call New Hyrule an element the games kept. Frankly it didn't and New Hyrule is about as much Hyrule as Termina.
With that in mind, if games are held to being excluded simply for being side-titles, MM, LA, OoA, OoS, PH and ST should all be held to that same standard. Out of those the only games that could still count for anything are the Oracle games which still have Ganon, the Triforce, Zelda, Impa and a Master Sword (if I recall). Seem fair? I mean FS/FSA contain a lot of those elements as well which by certain standards would give them more legitimacy than MM. I know that won't seem right to everyone. Heck, it seems a bit off to me.
Further to the idea of legitimacy, the way the timeline plays out suggests that the first 4 games would be redundant at this point because the 'defeated' timeline doesn't apparently work (I have a new head-canon on this that I need to work on). Call it nostalgia but I'm not happy to write those off.
I'll stop with the filler now, my answer is simple.
Of all the installments in this series, if nobody minds my being smarmy, I find the Hyrule Historia unnecessary. Pretty as it is, it doesn't inspire the same energy, imagination or satisfaction that playing any of the games do. In fact in certain cases it robs you of that.
All the games provide something to the series, whether you agree with what it gives or not. Be that World building, character development, story progression or closure.