Escape velocity is only needed for orbital flights. Going straight up and coming straight back down (like Virgin Galactic) can be done at any speed... but when the motor stops, even if you make it halfway to the moon, you’ll be falling back to earth, Wylie Coyote style.
Why we can’t “fly” into space is because of a lack of air for lift.
Yeah, because you didn't have escape velocity. That's why the word "escape" is in there. Once you've escaped you don't fall back: "It is the speed needed to "break free" from the gravitational attraction of a massive body, without further propulsion".