All Empires throughout history have fallen, no matter how glorious or powerful they were at their peak - it's logical to assume the Federation will at sometime fall too -is Burnhams surprise that it no longer exists nearly millennium into her future illogical? An understandable initial shock but also illogical given her Vulcan upbringing.
The Federation is not an Empire.
Empires usually spread through conquest and can end up too big to control - and besides, they tend to rule through fear and subjugation (none of which exist in the Federation) which usually lead to revolts/civil wars that tend to bring them down down the line.
The Federation doesn't work like that. Its based on diplomacy, freedom, equality/equity, free exchange of knowledge, technology, resources, and uses a policy of non-interference when it comes to internal affairs of alien cultures - alien species are in the Federation because they WANT to be, not because they are forced - and heck, alien species that do become part of the Federation do not lose their cultural identity... obviously, because there are social aspects for a society to manage which is needed to become a member of the Federation, some cultural changes ensue to ensure that the newcomers can 'function' as part of the Federation, but they tend to retain A LOT of their cultural identity as well).
If a first contact with a new culture is established, it gauges both sides more or less in regards to technological and social levels.
Not every species will be accepted into the Federation, and some baseline parameters need to be met on a social level... but the Federation doesn't force these things on others... they are a guideline.... something a society must be willing to do on its own in order to qualify for membership of their own accord.
This is why alien cultures are usually introduced to places like starbase Yorktown to demonstrate what life in the Federation is like.
Because the Federation mixes hundreds (and probably by the late 29th century) thousands of species, prospective member planets need to overcome social issues before joining to avoid or minimize such problems happening when they do become members of the Federation - otherwise, it wouldn't work.
And Burnham's shock at the prospect of the Federation falling is not unusual.
The Federation is an amazing idea... and I would imagine that alien species don't become members of the Federation for the perks alone or just because they said: 'We're bored, lets join the Federation to spice things up.'
Granted, some may have started off for different reasons (to get mutual protection), but that kind of mindset doesn't persist for very long when you essentially start creating a vast alliance between multiple alien species who had to learn to work together over centuries and travel to each other worlds to live and work there for personal betterment and betterment of others... so no, I don't think that something as big or quite like the Federation would fall apart internally. If anything, it would adapt/change and grow over time to become even bigger and better.
Albeit... in the 930 years, a lot of things that Burnham wouldn't/couldn't know about may have happened that could have brought the downfall of the Federation (such as massive interstellar conflicts that may have arisen or unforseen catastrophes)... however, it is highly unlikely it would be an 'internal' matter (aka, social aspect).. but more to the point an external one (a targeted attempt to bring down the Federation and potential species which could become part of it because someone or something may have considered it a threat given what it created and just how fast they are advancing as a result), or a simple accident of massive (galactic) proportions.
Besides, she was fresh out of a wormhole and 930 years in the unknown future while being cut off from her ship and crew.
Spock can be emotionally compromised and not necessarily show it... I think Burnham should be cut some slack.
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