I guess the YouTube channel you are referring to is ‘physics anonymous’ ? They are trying to build a homemade grinder but there has not been an update for a while.

I’ve been thinking about your question of whether alignment is relevant and it feels wrong but maybe you are right and it does not matter.

On the stiffness then as you say that will matter as the work piece will be pushed away rather than being ground and the effect will be different depending on where the table is on the rails as they are stiffer at the ends of travel. So the workpiece would not be flat but would be dished in the middle. Any reason you did not go for supported rail or linear profile rail?