You can put an edge on bronze. The problem is keeping that edge. You’d probably have to hone a bronze razor every half-dozen strokes – which would be long and tedious for shaving.
[hijack]
This is almost entirely off-topic, but I used to hate shaving until I started using a soap and brush rather than shaving cream. I’m not sure why, but it shaves much better for me. Maybe it’s just that it makes me take a bit more time with beard-prep, but I think that there’s more to it than that.
You can buy special soap, but I find that a particular brand of non-scented glycerin soap works well for me. I buy it at the local health food store (I believe it is cheaper than either shaving cream or the special soaps they sell for this, though I’m not entirely sure since the other two may last longer).
My experience with obsidian and other “glass” blades is that they are incredibly sharp…the sharpest I’ve ever handled.
But they dull more quickly then expected and of course are as brittle as glass. I suppose they can be resharpened by grinding, but I always just break off another piece or rework the edge.
The solution is to have more than one razor at hand. All may then be honed before the next shave. Remember, too, that you are just re-honing the edge between shaves…not quite sharp enough to shave is still pretty sharp. It’s not like re-profiling and sharpening a blade that has gone blunt.