Well, we haven't had a good disagreement or debate for a while, so I have to start one. :-)
Draws should not occur. Yes they would be quite rare in Poof Pente, but the fact that they WOULD be rare is a good reason to not have them at all.
You say that society is hooked on having a winner. That is correct. It is because society does not operate properly and efficiently in a socialistic or communistic state. That has been proven beyond much doubt. People are not born nor are any entities created equally. Any government or organization that attempts to make them that way is ultimately doomed to fail.
Everyone is constantly in competition with everyone else for either the betterment of themselves or their city, state, country, team, school, company, etc. In life, there really are no draws! Either one person beats another, one company gets the contract, one country defeats another in war, one state or country gets the olympics, etc. There are short-term standoffs in certain situations, but rarely does that standoff last for long because the 'game' really isn't over if there has been a standoff, it has merely been postponed.
So if a draw can be easily eliminated without affecting the inherent rules of the game, then I think that it should be done.