The good thing about a singlespeed is that chainsuck doesn't happen (unless something goes very very wrong). I am a little sceptical over chainline accuracy - if the chainstay (chain) length is circa 400mm, and you shifted the chainring over by 1-2mm so there is a slight misalignment between chainring and sprocket, it is 2mm offset in 400mm chain length - that cannot be significant. And on a singlespeed the only negative can be chain wear (really??) and noise (minimal). If you are misaligning the chainring by 5mm I can see why that is significant, but 1-2mm.......
I guess bear in mind that a geared bike only has good alignment in 1 gear (max) and not many people complain about the misalignment in the other gears.