To substantiate this remark:
The following establishes that while you can often show that a game equilibrium exists (Nash), you can’t appeal to a similarly universal statement that efficient dynamics enjoy the universality of Nash’s existence theorem
“Communication complexity of approximate Nash equilibria”
Or in other words, yes that is "… a very sweeping negative result,” and "If you’re trying to figure out if your game will easily find an equilibrium,…it’s on you to provide the argument why it would be.” Because, “If this is going to take longer than the age of the universe,… it’s completely useless, of course.”