One big thing that most junk science clips like this ignore is what has to be done at the other side.
When talking about traveling at speeds like this, it's very much like operating a car. It's not just enough to speed up, you also have to slow down at the other end. And when talking about in space which is a frictionless environment, you are going to need to spend as much time slowing down as you are speeding up. So if it takes you X number of days to reach velocity, it is also going to take you X number of days to decelerate on the other end.
We can even see this in our own lunar program five decades ago. Achieve orbit, then do a burn to gain speed to leave earth's orbit to travel to the moon. Then another burn on the other end in order to enter orbit around the moon instead of overshooting it. Then once again doing a burn to gain enough velocity to leave the orbit of the moon, then slowing down to not overshoot the earth and another burn to leave orbit and land.
Videos like this talk all about acceleration, but never seem to bother to mention the deceleration at the other end. Now deceleration on earth is much easier, as we have a lot of things like gravity and friction to assist. In space, you can only use the same engines you used to accelerate to decelerate. And at the same speeds.
