I've got an elderly Elektra Bekum KGS 300 mitre saw, like this Metabo (below, which is the later version, after Metabo bought EB). As designed, it has a sliding stop on the right and has only one work clamp (on the left). I couldn't find an image with the stop fitted, but it clamps behind the right hand fence, and is basically a U-shaped piece of steel rod, one end acting as the stop:
I realised recently that it was set up (or at least working) like my track saw - in other words there's a 'good' and 'bad' side to the cut. If the wanted piece is on the right, the cut is excellent (and true). If it's on the left, the finish is rough, and not true.
I think it cuts like this because the blade isn't perfectly in line with the slide and pivot. It's tilted slightly over anti-clockwise and possibly twisted clockwise (as you look down on it).
We're probably talking small fractions of a degree in both cases. In an ideal world, I ought to sort this out, so that both sides of the cut are right. It certainly limits its usefulness. But it would be a real fiddle to do, especially if it is tilted rather than twisted (big rubber mallet, lots of tapping and probably cursing).
I mention this because there's surely no reason in principle why you can't put stops and measures on both sides, BUT, if yours is set up like mine, one side will give much better results than the other.
E.
PS: Like Jake I'm left handed, but I occasionally use a push-stick to hold smaller work against the fence (on the right hand side). The EB/Metabo design is limited by the induction motor's position - the motor body reduces the depth of cut substantially because it's so bulky, and it's awkward to hold work underneath it - With small stock you can't see your fingers, which I think is dangerous.
Later: found a picture of the stop:
Mine has a wooden block on the end, and you can reverse the legs of the U for different distances - it's really handy for repeat work.