TL;DR: it is inefficient. You should play some Kerbal Space Program and see for yourself the effects of travel in this way.
Assuming, of course, you didn't really want to enter the orbit, but wanted to e.g. go to the Moon or deep space probing. Especially in conjunction with Wikipedia's note about not having to attain escape velocity to leave gravity well.
"Escaping", in the sense of what you'll do if you're travelling at escape velocity (and outside of the atmosphere) means leaving the gravitational sphere of influence (SOI) of a body. Obviously, gravity has effectively infinite range, but when you travel far enough from Earth you'll reach a point where the gravitational influence of the Sun far outweighs that of the Earth. You'll have escaped Earth, and entered into a heliocentric orbit.
The requirement for escape is therefore distance, not velocity. If you were travelling at escape velocity (and were outside of the atmosphere), the influence of the body's gravity will be insufficient to slow you to a relative stop and pull you back down, so that's one way to do this.
If you can imagine a pair of very widely separated worlds, joined together by a ladder. If you climb far enough along that ladder, eventually you'll reach a point in space where the gravitational pull of the world you started on has been exceeded by the gravitational pull of the world you're climbing towards. You'll have "escaped" regardless of how fast you can pull yourself along.
(note that if you're travelling to the moon, you don't need to be on an escape trajectory, because the Moon is still in the Earth's gravity well too. that means you'll be going at less than escape velocity, which will save you a bit of fuel)
So, what is the thing that prevents you from continuing the "getting to space is easy" mode of "going fast and then steering up", instead of trying to enter orbit?
The thing that makes "point up and blast away" a bad way to escape a planet is efficiency. Your rocket will be continuously subject to gravity drag... at every point of your escape, you'll need to run the engines hard enough to counter planetary gravity at that altitude, plus a bit more in order to move away from the planet. The longer you take to reach the edge of the planet's sphere of influence, the longer you'll spend having to oppose gravity, and the more fuel you'll waste doing so.
If you have a really powerful rocket so you can travel quickly to the edge of the SOI, great... but you could have just as easily pointed perpendicular to the gravitational field of the planet and run your rocket then, so the full acceleration of your rocket goes into increasing your velocity instead of a load of it going to opposing gravity instead. You wouldn't do this in an atmosphere of course, because then you'd spend a lot longer fighting atmospheric drag. So, you shoot more-or-less upwards to clear the atmosphere, and then you boost more or less sideways to build up lots of speed to reach the edge of the SOI as quickly as possible.
...and suddenly, you'll have found yourself emulating a fairly conventional rocket launch profile, albeit in a "direct injection" rather than the more conventional "enter Earth orbit then transfer to wherever" choice (direct injections are ever so slightly more efficient, but not really enough to offset their inconvenience otherwise).
(there's also something called the Oberth effect that means that using your rocket deep in a gravity well as close to your periapsis as possible is more efficient than using it much further out in an orbit, but one problem at a time).
The same about landings. Going to a celestial body, entering orbit, then having to shed all that orbital velocity. If you were travelling slow enough as it is, and slowly decelerating all the way, counteracting gravity
Obviously, if you're travelling really slowly relative to your destination, it'll take you a really, really long time to get there.
That aside, the issue is once again efficiency. The probably very non-technical term Suicide Burn is used to describe a landing trajectory where all your deceleration is done as late as possible, to minimise the amount of fuel wasted.
ETA: as neph observed, a direct descent trajectory is of course a little more efficient than injecting yourself into an orbit and then deorbiting, but presents timing issues if you wanted to land somewhere in particular and indeed safety issues as it makes bailing out back into orbit somewhat harder.