Why are 100% hexane or 100% ethyl acetate never used as eluents in column chromatography?
Why, of course you can, but most of the time one of them would be "too strong" and the other "too weak", so neither would work well for you. That's why you have to mix them to the right proportion (which depends on your system, and is found by trial and error).
Your comment is not entirely true. The solvent system used depends upon the behaviour of your (crude) product on silica gel.
Neat hexane (or a substitute such as petroleum ether or cyclohexane) is often used to wash 'grease' (non polar compounds) off the column, whilst neat ethyl acetate (or ether) is often used to elute highly polar compounds.
Ideally, you choose a solvent system in which the compound you want to isolate has an Rf of around 0.3 (please read the original flash column chromatography paper for more details), however, in practice, many chemists run 'gradient' columns. This entails starting with neat hexanes, and then slowly increasing the polarity of the solvent until the compound of interest elutes. This is also the way HPLC and automated flash (eg. CombiFlash/Flashmaster) works, using gradient elution.
Simply speaking you would often only use pure hexane (or better cyclohexane, as the former is somewhat toxic, or (cheaper) isohexane) to wash something completely unpolar off the column before further elution steps.
Pure ee you would use to just wash out everything that is still on the column after your chromatography.
Of course there can be the (i think rather rare) case where the polarity of either one is just what you want.