Calling Star Trek: Discovery nostalgic -- with one exception that I'll get to -- is calling Batman (1989) nostalgic or the Dark Knight Trilogy nostalgic. They're not. They took ideas from before and updated them for a modern audience. Except for "If Memory Serves", DSC doesn't look or feel like '60s Star Trek at all. Nor was it intended to.
The Klingons in DSC don't look or feel like Klingons from before. The only thing "TOS" about them is that they were enemy in the first season. That's it. Nothing else about them is like the Klingons from the '60s, '80s, or '90s. They were updated. In "Lethe", they were the scariest they'd been since TMP. In "The Vulcan Hello" and "Battle at the Binary Stars", the concept of peace with them at all felt totally, completely, and utterly foreign. Nothing like the Klingons from TNG/DS9/VOY. And they don't look like anything from TOS. That's not nostalgia. That's the opposite of nostalgia.
The Mirror Universe doesn't look or feel like the TOS, DS9, or ENT versions. It feels like a super amped-up version of the one we saw on DS9 except the Terran Empire was in its prime. They went further with the Mirror Universe on DSC than they ever would've on those other series. Again, that's the opposite of nostalgia. The only similarity is that it could get campy, but it was a dark campy. Which makes it feel more like the DS9 Mirror Universe than the TOS one.
Sarek's relationship with Burnham is completely different from his relationship with Spock. So even though we see Sarek, we see him in a different context. Not the same one. We see more of Amanda than we ever got to see in TOS and she felt more fleshed out.
Harry Mudd is arguably nostalgic. I can see that. But he's also portrayed as being more deadly. The Harry Mudd on DSC is like the Joker in the 1989 Batman while the Harry Mudd in TOS is more like the Joker in the Adam West Batman. Before someone takes that last bit out of context, hear me out: He's a horrible person but he seems harmless. Seems. Either way, the Joker was updated. And so was Harry Mudd.
When the Enterprise appears, that feels nostalgic. But only arguably so. They updated the look of it. It's not the '60s Enterprise. If it were truly nostalgic, every old-schooler would love it. That's not the case here. They didn't like the changes. In nostalgia, you're longing for things that changed. The Enterprise did change. So I argue it's not as nostalgic as some would say.
Pike. He was only in two episodes of TOS. One as an invalid and one where he actually had vitality. All well and good. But Anson Mount didn't play Pike strictly like Jeff Hunter. He combined Jeff Hunter's version, Bruce Greenwood's version, threw in a little bit of Shatner's Kirk while was had it, and then added in a lot of his own take. He made the role his own.
Spock. Ethan Peck's Spock is sufficiently different from Leonard Nimoy's that I didn't feel like we were getting more of the same.
Number One. Rebecca Romijin's take on the character was different from Majel Barrett's, even though they both effectively convey a hyper-efficient First Officer who does her homework, stays on top of things, and can give Spock a run for his money.
Anson Mount, Ethan Peck, and Rebecca Romijin didn't feel like they were just regurgitating Jeff Hunter, Leonard Nimoy, and Majel Barrett where as something truly nostalgic would've. This wasn't nostalgia. It was an update.
Then there's Talos IV. That's the exception I was getting to. Even though the production values were updated, they tried to still tried to make it feel like TOS as much as they could. It's like the Disco Enterprise, which also tried evoke TOS while still trying to adhere to the same aesthetic as DSC. Even people who don't like DSC felt nostalgic when they watched "If Memory Serves". It's the episode that actually struck that chord.
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Picard, on the other hand, has Jean-Luc Picard played by Patrick Stewart. Having the same actor play the same character is closer to being nostalgic than having different actors play the same characters in updated form. Except they also put Picard in a different place. We're not seeing Picard as he was when TNG was on in the '80s and '90s. Nostalgia would be ignoring the passage of time. PIC is tackling it head on.
So DSC updated TOS concepts for the 21st Century while PIC took TNG and has advanced it by 20 years. Either way, DSC and PIC didn't stick to keeping things exactly as they were in TOS and TNG.