"Time is the fourth dimension" is the single most damaging sentence for your understanding of time and space.
To have an n-dimensional spacetime where time is not the nth dimension makes no sense.
The video didn't expand on the person living in a 2D space example ... if such of thing would be possible, he would be able to explain the presence of a third dimension using time (going so far as to consider time as being the third dimension).
NO! Absolutely not! 2D spacetime does not look like 3D space at all!
In 3D space, I can take a 2D angle bracket, flip it in the third dimension, and get its mirror image. This will seem like magic to 2D creatures. In 2D spacetime, I can do no such thing. No matter how long I wait (i.e. move in the third time dimension), the angle bracket won't transform into its mirror image.
In 4D space, I can take a 3D right-hand glove, flip it in the fourth dimension, and get a left-hand glove. This will seem like magic to 3D creatures. In 3D spacetime I can do no such thing. No matter how long I wait, a right-hand glove will never transform into a left-hand glove.
Do you understand?
Do you see how adding time to n-dimensional space does absolutely nothing to explain n+1 space?
But it's early in the morning and I haven't had breakfast. Talk to you when my brain joins me.
To perceive time as a dimension is useful because it helps you realize you actually perceive four dimensions the same way a flatlander perceives three.
If you want to do space-time calculations, yes.
because it helps you realize you actually perceive four dimensions the same way a flatlander perceives three
Absolutely not. We perceive time as time and space as space. The concept of spacetime does not help us understand or visualize higher dimensional spaces at all. It only confuses the issue, which is exactly the original complaint against the video this whole discussion is about.
Edit: One more example: Can you visualize the difference between a 3D cube moving in time, and a 4D cube moving in the 4th dimension? If you project the 4D cube down to 3D, it will look like a double cube that twists itself inside and out, but the 3D cube moving in time will just look like a 3D cube. Spacetime does not help you understanding 4D space.