hehe - there is no such thing as a left centered straight stitch machine - when you have a round hole, left or right gets you broken needles.
There are many japanses made zig zag machines that have the needle all the way to the left in straight stitch mode, and then as you widen for zig zag, it goes from the left to the right- farther as the zig zag gets wider.
With most LRC machines, you can put the needle to the left and then it will perform the same as a left centered machine, so if you have a pattern zigzag, you can get a different look as it will all line up on the left and vary on the right.
What I don't like, my Kenmore is an off center homing needle.