Vitalik has mentioned this in a comment but I think it ought to be expanded upon:
Companies that aren't already penny stocks really don't stand to gain anything from trying to prevent short interest. Short selling does not inherently lower the stock price - not any more so than any other kind of selling. When somebody shorts a stock, it's simply borrowed from another investor's margin; as long as it's not a naked short resulting in an FTD (Failure To Deliver) then it does not add any "artificial" selling pressure.
In fact, shorting can actually drive the price up in the long term due to stops and margin calls. Not a guarantee, of course, but if a rally occurs then a high short interest can cause a cascade effect from the short "squeeze", resulting in an even bigger rally than what would have occurred with zero short interest. Many investors actually treat a high short interest as a bullish signal.
Compare with margin buying - essentially the opposite of short selling - which has the opposite effect. If investors buy stocks on margin, then if the value of that stock decreases too rapidly they will be forced to sell, which can cause the exact same cascade effect as a short interest but in the opposite direction. Shorting is (in a sense) evening out the odds by inflating the buying pressure at lower stock prices when the borrowers decide to cover and take profits.
Bottom line is that, aside from (illegal) insider trading, it doesn't do businesses any good to try to manipulate their stock price or any trading activity. Yes, a company can raise capital by selling additional common shares, but a split really has no effect on the amount of capital they'd be able to raise because it doesn't change the actual market cap, and a dilution is a dilution regardless of the current stock price. If a company's market cap is $1 billion then it doesn't matter if they issue 1 million shares at $50.00 each or 10 million shares at $5.00 each; either way it nets them $50 million from the sale and causes a 5% dilution, to which the market will react accordingly.
They don't do it because there'd be no point.