"Because, even with near FTL speeds, an invasion can be detected and eliminated while in-flight. It's not like the invaded people don't have years to detect what is coming. And you need to move enough people, supplies, and weapons to invade a whole world, which would likely hit that energy barrier you mentioned, and then control the people you sent invading, since direct control is not possible."
When I'm given the choice between certain death by staying here and probable death by invading a nearby settlement, I'm choosing the latter.
"People will still make, buy, and sell stuff, so profit is still possible"
This is literally one of the most basic concepts in economics, 90% of the time people use the phrase "this is Econ 101" they are lying, however I am not joking when I say you are taught why you are wrong in Econ 101. For a corporation to remain competitive in the long run their profit will approach 0.
Say I'm selling widgets and make $2 of profit for each widget I sell. Assuming there is no law preventing competition and no cartel using the threat of violence to maintain their oligopoly then John Smith, seeing that I am making a full $2 of profit can start an identical corporation selling widgets for a profit of $1.90, I'll have to lower my prices or go out of business, thus I'm going to start selling widgets for $1.85 profit, John will now sell them for $1.75, etc. etc.
Now keep in mind in a zero sum economy competition becomes more vicious (as its guaranteed that if someone doesn't compete they starve, as if we include a welfare state it will no longer be a zero sum economy but a negative growth economy. As if someone doesn't work, he doens't lose out but someone else does, eventually nobody works cause if you work someone else will profit from said work so why bother) so the long run happens more quickly.
It is 100% impossible to make any profit in a zero sum game without the use of violence to achieve your end.