-Proof of Stake would help secure the network and protect from forks (like the one that happened).
-It would encourage people to hold their coins to earn stake reward and take those coins off the market. Usually this has a very very positive effect on price as has been the case for most PoS coins. (clam-rby-etc..)
-It would make whales much more interested in being involved due to not worrying about endless inflation from PoW mining.
-PoW coins are very hard to raise the price on and keep the price up due to daily mining dumps and lack of investor interest. See coinmarketcap.com for top 50 coins that are PoS, not mined, near fully mined.
-PoS inflation could be 5-10 percent a year whereas PoW inflation (3 percent per MONTH - 36 per year) dumps .125 btc a day to the order book. At 1 million dollar market cap that would be 2.5 btc per DAY.
-Generally miners will be pro PoW since that is their income (mine and sell daily) and PoS will appeal more to investors who want the value of a coin to rise and preserve that value as an asset.
-PoS is perfect for a coin that is connected to a service like this trading software. It will make it much more appealing to hold while using the bot instead of worrying about high inflation lowering price.

PoW is like endless printing of shares of a company -- PoW is more like an actual investment
(BTC exception granted )

etc...etc...etc...