> I don't see why it would not be admitted.
Inability to come to mutually agreeable terms -- Scotlands wants (1) essentially automatic admission without the normal new state process, and (2) to keep the UK's special exemption for using the sterling, and (3) to get part of the UK's rebates.
AFAICT, much of the rest of the EU is opposed to all three of those. Spain is particularly opposed to the first (and possibly to Scottish admission at all), because an independent Scotland getting into the EU, especially on fast-track process, is seen as encouraging Catalonian independence.
> The EU is not in the habit of turning down that kind of country: wealthy, peaceful, of Christian heritage and adjoining several EU countries.
First, I think you are considering the wrong category: the category of interest is "states having recently broken away from existing EU member-states", particularly as the UK isn't the only EU member with regions that have some pro-independence sentiments, and admitting such a breakaway state is something that states that have their own aspiring breakaway regions are likely to see as providing encouragement to those breakaway regions.
Also, an independent Scotland would be adjoining exactly one other country (the UK), and one of the reasons that seems to keep being cited for it leaving is that, even with Scotland still in the UK and exerting pro-EU pressure, the future of the UK in the EU is locally considered less than certain, so I'm not sure where you get that "adjoining several EU countries" is a fair description.
> And if you want to play that game, it's not certain that England will remain in the EU.
Of course its not; I don't dispute that at all.