Shatner doesn't despise Kirk like Stewart does Picard. He's forever butt blasted that he, Sir Patrick Stewart, a classically trained theatre actor, is going to be remembered most for sci fi schlop.
The frustrating thing about Steward is, he was on a trajectory very similar to Brian Blessed. They were both hammy character actors, in their own unique ways, both got a couple couple of lucky breaks (both played in I CLAVDIVS, whose alumni have all gone on to great things), but where Blessed embraced his eccentricities and ran with every opportunity he was given, Stewart had a streak of arrogance to him that meant he thought himself in some way above the material he was working with.
It's down to the fathers, I think. Blessed had a great relationship with his dad, whereas Stewart's father was an abusive and violent man. Something of that might reflect in why he kept pushing for Picard's character to be more of an action hero sort; he was still, unconsciously, trying to prove himself superior to his father, trying to prove that he's a real man and not a beaten child. Meanwhile, Brian Blessed doesn't have to prove anything to anyone. He just turns up and shouts a lot.
I've been re-watching TNG from the start again, and just got up to The Drumhead - I totally forgot about this episode and just how incredibly nuanced the writing is. It's still a bit cheesey, but that final scene really does stick with you.
https://youtube.com/watch?v=CbQvCzWkATA
The fact that episode is so popular is proof that when people say they don't want politics in their shows, what they really mean is they don't want
lectures. TNG addressed political issues for almost its entire run, which means that some of its worst episodes are dismissed as "too political", but then some of its absolute best episodes were also intensely political and didn't suffer the least for it, because they treated the viewers as intelligent and rational beings, instead of speaking down to them like they were retarded children.
That's the problem with NuTrek in general. Even Voyager, for all its faults, tried to treat political topics with nuance and fairness, rather than just browbeating the viewer with the acceptable way to think. Most of the time, anyway.