As someone who played the whole trilogy but has never read the books, and is just about to finish TW3, I have to say the one persistent and clear problem with TW is how bad it is at handling the "existing lore" stuff. Every game, you finish it without a clear understanding of important aspects of the story, and you have to just give up on questioning why some of the things are the way they are. The player has to simulate a knowledge he does not have, and just presume that the big holes and gaps are covered by the books. This is bad - and I think TW3 is more egregious here than TW2.
For instance, if the player knows nothing, then they get literally 0.5 mentions of Ithilenne's Prophecy until you reach Kaer Morhen and Yennefer uses the megascope, etc. Sure, you find the Prophecy book at notable points in the main plot, and a couple of dialogue references to 'the prophecy', but that's completely inadequate. Geralt and Yennefer are supposed to know about Ciri. So why is the player never told, in many natural ways that would have been easily possible, what is going on? You are not told of Ciri's powers' relation to the Prophecy. You do not know who the Wild Hunt are, why they pursue Ciri, or why they need the Prophetic powers. In fact, the Wild Hunt are the main antagonists here and also feature in TW2 but you learn basically nothing about them. You also don't learn why and how Ciri was in Geralt's care as a child, when and why they were separated, whether she is even the biological child of Emhyr. Literally all you get is tiny little pieces: Geralt's quip to Emhyr in their first meeting that he didn't give a shit about Ciri before, for example. Geralt even quips near endgame "when I rode with the Wild Hunt", which threw me for a loop. In short, you just have to say, I have no idea who this girl is or why we are pursuing her but I suppose I'll find out - and you do, after 50 hours, though only in the most basic sense. This is ridiculous, and severely hurts the story.
This is a chronic issue in all TWs, but is much more prominent in TW3. In TW2, it was easy to work out the lines of international tension in the politics of the North. You had no idea what Nilfgaard was or what they wanted, but they weren't important to your experience early on, and you gradually were shown more about them. You don't need to know exactly what the Lodge is, etc. to get to grips with the story unfolding in front of you. You have a good grasp of why and how the nations are in conflict, how Foltest, Radovid, etc. differ in their outlook, why the sorceresses might be the object of hate and jealousy, why Radovid blinds Philippa Eilhart, etc.
Even apart from this lore-handling issue, TW3 story is weak and too epiclulz. The Wild Hunt are never compelling. Even aside from the fact that I know nothing about them, their aesthetics just scream "NAMELESS EVIL ROAR WE ARE SAURONS MEN". The generally good quality of the writing is punctured by a singularly cringy line near the end - "Humans, so impractical", when Vesemir is in danger. Seriously? You might as well just make them into Orcs, or into Pokemon's Team Rocket (or whatever they were called). You also spend far too long in the game not having a clue what the fuck Ciri is doing or what is happening. I thought the final discovery of Ciri was really well done, and the fact that you find her so near the end works well, but the political plot of the North against Nilfgaard and Novigrad's persecution of nonhumans should have become more dynamic. I expected something to happen in the war front and for Geralt to have some involvement, but basically nothing happens aside from Dijkstra's plot (you can't actually participate in the mission, right?), and Radovid is reduced to a questgiver hanging about for your report, as is Emhyr. The Triss / mages sequence and subsequent persecution is done well, at least.
The really strong parts of it, as others have pointed out, are the side characters. The Bloody Baron questline is probably the high point of the entire game - wonderfully done, with great writing and pacing throughout. Dandelion's quests can be annoying, but I liked the bit of lightness it brought (as a Dandelion questline should), including the little theatre acting, and it also brought the various storylines and characters in Novigrad together very well. Triss again was good thematically for reasons stated above. The an Craite / Skellige succession sequence was also a really good way to bed the player into Skellige, both its human civilisation and its specific kinds of legends and monsters. There are also a number of sidequests or little moments that stand out and give the unique TW vibe - such as the Leshen contract in Skellige where you have to choose between killing a marked villager girl (& support the less savoury villagers) or side with a likeable elder & perpetuate the fear of monsters.
I skipped quite a bit of content to leave it for an immediate second playthrough, but do you need to use a TW2 save (or pretend it) to find Letho?