The point is that a child who is never asked to do anything even vaguely difficult will develop a self image and sense of self that says they do everything effortlessly. The first time they come up against something they can't do without thinking they collapse and refuse to even try. There is research to show this.
In life, it's effort and willingness to get up, dust yourself off and try again which helps you succeed. And I'm using succeed here to mean being a happy, contented, confident person. Those are not skills you just magically acquire, you have to learn them.
It sounds like your wife experienced this, as I and many others on here did. For me, it was at university where I finally encountered something difficult, so I shut down and walked away.
You experience tells you that college at fifteen is not great, so don't send your kids at fifteen. Send them to tend bar on the ski slopes in Canada for a year, get them to do some Coursera or edX courses while they perfect their golf swing. Whatever, but just because someone completes high school doesn't mean they need to go to college the next year. Hell, maybe your kids will stay in high school doing all the subjects until they're a more common college age.
Some things you might find informative to google are "zone of proximal development" and "the calculus trap". There's also an article in the NYT called something like "don't tell kids they're smart".
