That's a pretty close definition, Tony. And your comment about the trained fighter is one I've made, too. If I do randori with someone trained in a grappling art, much of the aiki opportunities go away. If they are trained in an aiki art, they should be able to remove pretty much all of them unless I'm a lot more skilled than them.I think we're on the same page regarding aiki. It's that moment when you feel like your opponent is throwing himself and you're just helping steer where he goes with no effort whatsoever. I've had that happen occasionally in sparring. Generally it's been a moment when my sparring partner comes forward with a little too much commitment and I've been able to blend with his energy while applying a Judo technique like Harai Goshi or Tai Otoshi. It really does feel magical.
The thing about those occurrences is that they are dependent on the other person screwing up and providing that over-committed motion at a moment when you are prepared to take advantage of it. A skilled fighter is not going to provide very many of those opportunities. That's why if you put a master of an aiki based art into a cage fight he'll have to use something else 99.9% of the time.
Presumably an untrained attacker in a street assault would be more likely to provide those opportunities. However I think it is a mistake to train under the assumptions that the option will always be there.
BTW - my theory about the purpose of the Nage no Kata in Judo is to provide a reminder to be ready for that "aiki" moment when the opponent gives you exactly what you need for an effortless throw. In competition a judoka will be facing a skilled opponent who knows how to maintain a solid base and will be unlikely to put himself off-balance. Therefore Judo competition becomes more a game of forcing that off-balanced moment and it's possible to forget about the possibility of an effortless throw being just handed to you on a silver platter.
One distinction is that it is possible to nudge someone into an aiki moment. It doesn't work well with trained fighters, because they've replaced many predictable reflex responses with movement into techniques. With untrained individuals, however, their range of responses to some input is more predictable. I verify this when I get a new student who has no (or at least little) prior training. I can verify parts of it even with folks trained in other arts. For instance, those who train in striking only tend toward some reactions more than the untrained population, and more reliably than those with a grappling background.
And many of the things that cause aiki opportunities just don't come up in competition. If someone reaches for my phone/wallet/the knife I just managed to take away, they use a motion (and level of commitment) that's unlikely to occur in any competition. The same goes for a barroom shove, or an enraged tackle. All are good examples of movements unlikely to have close analogs in sparring or competition because the opponent is purposely maintaining control of his body to avoid giving those opportunities.
As you say, it's not a good idea to assume those will always be handy. This is my problem with some of the stylized drills used in some aiki arts. If they are used too often, you're only training for aiki movements. I teach versions of techniques that I refer to as "the Judo version" as a shorthand for indicating there's no real aiki "void" there, but a good place to apply leverage and technique that they can't easily counter. I also teach students that if they head toward a technique and it goes away (meaning the opening vanishes) that their first response should be to hit them. This is an oversimplification of the principle, but it gets new students away from chasing aiki and into finishing the defense.