The top I believe contains the methanol, which is poisonous. They have to separate that, otherwise, their consumers would dwindle drastically.
Is it really that hard to have pure alcohol though? Is there not substance in stills that could ensure a very high purity. Would distilling it multiple times help? Obviously, the mash is ripe with impurities, but the distilled spirits from it could be distilled against for even further purity couldn't it? Or do stills have some nature of no matter how many time, you're always going to get contaminants from the material and such?
I suppose the same could be asked about water too.
Producing pure alcohol isn't entirely difficult. In essence, that is exactly what Everclear (190 proof) and "moonshine" (I reckon proof varies) represent.
"Neutral grain spirits" essentially equals "pure ethanol".
The fear from moonshine is the likelihood that they don't have much testing equipment and aren't technically masters at their craft, so it's likely they've not separated the heads and tails all that efficiently (if at all). There's nothing about moonshine production itself that makes it potentially dangerous, it all rides on the expertise of the 'shiners.
The legal definition of vodka is basically: go produce everclear, and water it down.
It is, however, the only liquor classification that follows that route. Most other liquors utilize stills, but few if any distill to the point of essentially pure ethanol, and most have varied production methods that are focused on imparting character, which, by definition, is what products like Everclear and vodka fight so hard to avoid.
So, for your question, it's not really hard to produce pure alcohol. There is little reason to do so, however.
BTW: the starting proof of vodka, and the final proof for Everclear, are essentially the purest you can get using the basic still process, IIRC. 190 proof = 95% pure ethanol. I think, chemically, producers can get to 100%, but it might be far more volatile, and more importantly, it involves more steps after distillation. I might be wrong about the 100% point, but I don't feel like looking that up again. They can get it higher than 95%.
Most of the time, however, outside of vodka and standard grain alcohol, any such pure ethanol production is going to be not judged to the critical standards of human consumption. It's relatively simple to produce ethanol to that level, which has many industrial and economic purposes, but I have a feeling many of those applications it isn't critical if every last molecule of methanol or the other alcohols are removed.
Even then, once you get into the chemistry approach, I think it's on the level of stupid easy to actually strip every else out.
It's also stupid cheap to produce ethanol in large quantities. It is sold, denatured (which means methanol is *added*), for an absolute steal.