While I agree that a bit alone is not a solution to a training issue, I think it's worth investigating whether a different bit might be more effective for your situation. If your horse is not willing to soften to it no matter what you do, he might just be uncomfortable with it at this stage of his training. Have you tried other bits within the snaffle family? Different rings, (egg butt, loose ring, d-ring), different thicknesses in bits and different types of middle pieces? I recently went through a bit change with my boy, not because he was not listening to it, but he wasn't completely happy with it either. It was a subtle change. We went from a D-ring french link to a slightly fatter loose ring french link. The difference was immediate.
If you know how to walk your horse in hand, walk next to him at his shoulder and hold the reins as you would if you were in the saddle. Pay attention to what he's doing with the bit as you walk along on contact. If you see him trying to push away the bit with his tongue, he might just not like it. A lot of horses seem to be liking those bits with the fat middle lozenge piece.
I seem to be rambling now. My point is, it can't hurt to investigate a little. The only time it would be wrong to switch a bit would be if you were doing it solely to "teach the horse a lesson". You're clearly not doing that, so my 2 cents is, switch away!
You just have to see your distance...you don't have to like it.