The only advantage is time. If somebody doesn't have means of pkhex, they will have to spend more time, but they can make the exact same pokemon as somebody who does, statwise, ability wise, etc.
I recommend you look up more information on how Pokemon stats work, such as EV (Effort Values) and IVs (Individual Values). Those are what are being referred to. That would answer your question.
Long story short, you could, in theory, have all 510 by level 2 if I"m not mistaken. Through sinking a lot of money through various "EV items", you can provide all the EVs to a Pokemon and just have it level up to gain them.
If I'm mistaken on how items like those work (Protein, etc), I know for a fact you can do it by a low level regardless by a series of low level Pokemon encounters. I'm sure it isn't a stretch to have everything by 15-20 doing it the old fashioned way.