Binance seem to be firmly in the market of SHA256 hashing, so I guess they will mine whatever is profitable.

If they're interested in long-term survival of BCH, only time will tell. I would not put too much weight on the recent profitability dip in BCH. Binance has been mining BCH for quite some time. There isn't an indication that they are not in the BCH mining field for longer. But just like some major miners mine BTC which they may sell for BCH, others may mine BCH while selling for other coins. Binance certainly has closer ties to its own exchange currency than to BCH. That's just common sense.