From the very article you reffered to me :

Short sellers were blamed for the Wall Street Crash of 1929.[15] Regulations governing short selling were implemented in the United States in 1929 and in 1940.[citation needed] Political fallout from the 1929 crash led Congress to enact a law banning short sellers from selling shares during a downtick; this was known as the uptick rule, and this was in effect until 3 July 2007 when it was removed by the Securities and Exchange Commission (SEC Release No. 34-55970).

So one is actually entitled to wonder if regulations are not needed. While the article fail to explain categorically in which way it is "incredibly important".

There's a really big difference between blaming short sellers for the crash, and short sellers actually being the cause for the crash. Short sellers got blamed, but weren't necessarily at fault. There's a further implication that the crash is the cause for the Great Depression, which is likewise fairly unfounded.

If there was short selling that could have been blamed for the crash of 1929 it was what is known as a naked short selling. Since non-market making short selling now requires having a locate, it is impossible to sell short more shares that one can reasonably borrow.