The most common need was that many altcoins would start off with a large premine, and then they would offer an IPO/ICO/CFC (depending on the time, the term for this would change to be whatever was least likely to get the SEC's attention) where they basically put all the coins on an exchange or with an escrow and make it so that people can buy the coins in exchange for bitcoin. If they don't sell out of the altcoin's supply, then the developers are left with a number of coins. These coins are typically destroyed so that the only supply is owned by people who bought into it.
That problem isn't destroying coins though, it is verifying that coins have been destroyed. A person can destroy them easily, verifying that someone else is destroying them is hard.
The whole situation you described is completely ridiculous though, because instead of 'destroying' coins the developers could have distributed their own coins to all other addresses proportionately based on balance.
The whole thing is an obvious scam from top to bottom, but I'm not surprised any more that some people would take the bait.
if you give out free coins you are decreasing the value of your coin. if you destroy them, you are theoretically increasing the value.
since the popularity and value of these things are very correlated, it makes way more sense to destroy. Who is going to spend real currency on a coin that is losing value day 1 because everyone has coins to sell?
If you give out coins exactly proportional to balance the value per coin has changed, but hasn't changed the distribution. It's like multiplying all balances by 100, it's just a unit change.
