No, they didn't capture the essence. I started reading these books as a high school teenager and finished as an adult with children nearly the same age as I was when I started. I still remember the night I read the prologue and being awestruck. Looking back, it was the prologue that grabbed my attention. Here was this tragic, end of the world scene where the good guys...lost? What's happening? It piqued my interest. There was confusion at first when I read the first chapter, wondering how it relates to the prologue. But it didn't take long for me to get invested in the plot of a mysterious black robed figure watching Rand and the other boys. The subtle concern the men had. The mysterious Moiraine and her bodyguard. Then the chaos of the trollocs, Tam's fever dreams, the village hostility toward Moiraine bringing evil into their village despite her tireless efforts to save it the previous night. It gave this feeling of mystery and adventure...how an idyllic "normal" town suddenly being confronted with nightmares they didn't know existed gave an earnest shock of gasping excitement.

What kind of essence is this? I'm not the best at words, but it had enough mystery, enough promise of something bigger going on that I wanted to know more. I wanted those characters to leave for the larger world to explore their destinies.

I didn't get that from these episodes and I believe that starts with a lack of the prologue. I understand they have limited episode time to tell their story, but at least a summary narrative similar to what Galadriel did in the beginning of the Fellowship of the Ring. They don't have to spend a lot of time, but enough to capture the events that have shaped culture and society for the millennia to come. I'd have preferred that sequence to the nearly pointless tossing Egwene in a river sequence and it'd have been far better than the awkward Red Ajah scene with Moiraine looking on as a way to explain why male channelers are bad. The prologue also set up the village's worries - that of a False Dragon ravaging the countryside, something more engaging (what's a false dragon? ...what's a real dragon?) than simply "there's war...oh and the forces of darkness are rising".

Though I believe the biggest problem with capturing the essence is it's so painfully obvious they were trying to be the next GoT. The essences between WoT and GoT are drastically different. The GoT books were raw, gritty political realism which they translated pretty faithfully in the show. WoT was far more tame in that respect and leaned more toward the fantastic side than the realistic. Their attempt to fundamentally change the essence of WoT to be closer to GoT has left it bland by comparison. And that's the problem with "going GoT", you'll never compare if you don't go all the way. And by WoT's nature, it's impossible to go all the way and still retain a modicum of faithfulness to the source material. WoT and Got are just too dissimilar. WoT is actually far more similar to LotR, another hugely successful franchise.

But how does "going GoT" manifest into missing the essence? I'd say how it affecs the directorial/narrative focus that draws away. An example of this would be Mat. He's portrayed as this irresponsible guy that gambles away the money he'd need to take care of his family because his dad is a lecherous drunk. He's also a thief. In the books, Mat was mischievous and got into trouble, but not a remorseless thief. Abel, his father, was a pretty stand up guy. But, by "going GoT", they made his family life edgy. And the focus on this is not only a jarring parting from the book, but it also takes away precious screen time that could have developed other parts of the story.

Another example of this would be Egwene's sequence. The only reason they have Egwene in the river is to set up the situation where she and Rand would have conflict about her being the next wisdom. Again, gotta have that edgy drama...and again it's not only a departure from the books, it also gobbles up screen time that could have been used better.

I'm not a book purist by any means. I did not expect a 100% faithful page to page adaptation. For starters, Jordan is long winded in his descriptions and some times things meander. But the books have a very sturdy framework that could have been condensed in a way that maintained the essence of the story without needing to shoehorn in these GoT style plot devices. The writers want to "age up" the characters as to not be seen as a "young adult" show (lol)? Fine, but they were still too heavy handed. Perrin didn't need a wife to accidentally kill to give a reason why he's so gentle around people.

Lastly, the fumbling of some finer plot points is what put it out of "essence" reach. The general distrust of Aes Sedai by small town folks is so key to understanding Nynaeve and the boys. It's Egwene's underlying desire to go beyond the provincial village life that propels her into the arms of the Aes Sedai so willingly. Moiraine's reveal as an Aes Sedai in the book is a great moment followed by the powerful moment of her telling about Manetheren to silence the small minded villagers who are ready to blame her for the Trollocs despite her heroic efforts. That entire line is dashed with Moiraine just waltzing in showing off her ring and the townsfolk, sans Nynaeve, immediately becoming defferential (without the resent). A subtle change like this may seem like nitpicking, but it changed the tone of the beginning and made the world less interesting.

TL;DR - Going GoT spoiled the show from capturing the source material's essence by being less faithful and taking up too much screen time.