Agree with your second point. If the city with the highest science bonus is not your highest science city (leaving aside the question: how on earth did that happen?), you should rush buy your, e.g., lab in the city where it will have the highest impact on total beaker output.
As to your first, I agree that a Tradition capital has an inherent growth advantage (and head start) vs. any other generic city (even before accounting for the fact that an observatory city will often have fewer food tiles than a city settled in the open). That said, if your capital is going to struggle to grow, and you can quickly settle an observatory-eligible city that will ultimately far outstrip your capital's population, a player should be open minded about where to build NC.
As to your first, I agree that a Tradition capital has an inherent growth advantage (and head start) vs. any other generic city (even before accounting for the fact that an observatory city will often have fewer food tiles than a city settled in the open). That said, if your capital is going to struggle to grow, and you can quickly settle an observatory-eligible city that will ultimately far outstrip your capital's population, a player should be open minded about where to build NC.