Binance will indeed do anything to keep BNB at a stable price, including price manipulation which often occurs on Binance. This has become a natural thing for those who have an exchange business, many will definitely do that. It depends on us as internal people who do it cleanly or not.
Stable price? I don't think so. I believe Binance wants to find every way to support the increase in BNB price. BNB is the native token of the BNB chain and has utility on Binance CEX. BNB price depends on the demand of users and investors. It is not a stablecoin with a price pegged to USD or EUR. The increase in BNB price not only makes the BNB ecosystem more vibrant, but also helps Binance CEX to have more users, revenue and profit.
I believe that as long as Binance exists and is the largest CEX with an extremely attractive launchpool and launchpad, BNB price will continue to be supported and grow well, bringing profits to investors.