Not sure which video you mean. Tubalcain has a bunch of videos on this, and most of them are maddeningly over complicated.
Are you referring to this one?
Here is the issue trying to re-use the test bar in a three jaw chuck.
If you put raw stock in the 4 jaw, the machined end will never be concentric to the part clamped. This is because the raw stock it not round. Even if you centered it to 0.0005", it will still only be that close to center on those 4 areas that are clamped. The 3 jaw will clamp on different parts and the spigot will not be on center. Clamping marks and distortion will lead to further error.
You would have to put stock that is already machined round in the 4jaw, and get it perfectly on center, then turn the spigot. Since you will never get the stock perfectly on center, it will always introduce some error, the error will compound. You would need to turn a new test bar each time you used this method.
You will notice that Tubalcaine is not putting it in a chuck, he is using the headstock MT.
Really though, anything that you are comfortable with, that is actually aligning the axis of the spindle to the tail stock is fine.
All that is important is that they line up close enough for the kind of work you are doing. If you are doing very precise work that requires a great deal of repeatability, then nothing beats a taper test - it is how the machines that make test bars are aligned. If you just need to support the end of longer stock or drill holes, it is enough to bring the points together with a scale between them. this will get the alignment to under 0.001" in the same amount of time it takes to loosen, adjust, and tighten the tail stock.
The "best" method for this is the method that brings you the most joy (or least frustration), and does the job well enough for what you are doing. Getting the tail stock in under 0.005" alignment is a waste of time for most work, but doing this brings many of us more enjoyment (myself included).
The "scale" method I was referring to is an old school way to align the tail stock. You just put a center in the head and tail stocks, and bring them together with your pocket scale between them. Any mis-alignment will cause the scale to cock at an angle. If the points are in perfect alignment, any flat thing clamped between them will sit perfectly perpendicular to the axis of the spindle. I do not align my tail stock this way, but I do use it check alignment before I turn between centers.