I don't think it looks easier to do this with a normal trash bag, but maybe it's easier for a smaller can?
A guy on TikTok has a great trash can lining hack. Instead of stuffing the bag inside the can and then pulling the rest over the sides, he puts the entire bag OVER the top of the can, and then he pushes it to the bottom so there are no air pockets.
They say it works best for grocery bags that you put in small wastebaskets.