Is there a downside to publishing the same blog in multiple places, like blogger and wordpress simultaneously? Is it bad to fragment my traffic like that? Any thoughts?
Better to focus on one blog at one place and devote all your energies to it. Make a choice and stick to it.
One good source is many times better that two equal. If your goal is traffic then stick to one with original quality content.
my only thinking was that perhaps a certain number of people would be much more likely to follow a blog on a platform they are familiar with...like if you know blogger, you'd be more likely to follow a blogspot blog than a wordpress blog...
That's a misconception and a silly sounding one at that. If the blog is good, it doesn't matter what platform it's on. Platform choice matters only for your convenience and ease and such.