I enjoyed this comedy episode...
But I don't know if I can really support the plot. Isn't the point of Vulcans that they experience emotions so intensely that they have to control them severely or they will hurt themselves and others? Why do all the humans-made-Vulcan have all the emotional control that Vulcans spend years learning from birth to young adulthood?
The question of what Vulcans are supposed to be like really depends on the writer. Spock in the original show is honourable, kind, thoughtful, caring, but has a peculiar and eccentric way of showing it. However, nearly every other Vulcan we meet on the original series is condescending (Sarek), detached (T'Pau) or outright malevolent (T'Pring); there's the sense that Spock is an atypical Vulcan and also half-human. It's hard to say what Vulcans are "supposed to be like" as it's a moving target. Tim Russ' Tuvok was very much of the Spock mold in demeanor, but Russ' performance and the writing (occasionally) added quite an edge: Tuvok was manipulative, sarcastic, a bit ruthless, albeit not very consistently as the writing could be painfully generic.
ENTERPRISE, despite rendering Vulcans as being a lot like Sarek or T'Pau or T'Pring, is often criticized for its (admittedly underwritten) Vulcans in Seasons 1 - 3 and lauded for offering an 'explanation' in Season 4 for why the Vulcans weren't more like Spock, which has also muddied the waters a lot.
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I think the SNW writers are obviously fans. They've taken some liberties like with the Gorn, but the references to Vulcan cuisine (tasteless soup), the explanation for why the Eugenics War has been pushed back, the use of Roger Korby and Trelane, and the details regarding Kirk's son are obviously indicative of deep familiarity with the series even if they're using the Temporal Cold War to justify continuity shifts.
I would also note: "Tomorrow and Tomorrow and Tomorrow" implies that the reason TOS and SNW continuity don't match up is because the Romulans have, in the Temporal Cold War, repeatedly attempted to erase the United Federation of Planets.
The Federation is the core continuity discrepancy of all the early Season 1 episodes of TOS: the Federation doesn't seem to exist until Season 1, Episode 18. It's only after that point that constant inconsistencies with the era (22nd or 28th century?) and Kirk's employers (United Earth Space Probe Agency, Star Service, Space Command, Spacefleet) seem to solidify into an undated future (later said to be the 23rd century in WRATH OF KHAN) and Starfleet. The fact that the writers chose this one specific target for the Romulan time travellers to explain discrepancies indicates a deep familiarity with the source material.