According to Espressif website, current "reference price" for S31 sample module (1 piece) with 16MB flash + 16MB RAM is $6.2.
If S31 won't be much more expensive than S3 in bulk, it has a chance to become a very successful and what's more importantly really cheap full-featured Linux platform, in a small form factor, with flash, RAM, and radios integrated.
Espressif here could easily kill many contenders. You can count Wi-Fi-integrated Linux SoCs on one hand, let alone with RAM+Flash integrated, let alone cheap and available in quantities, and with reasonable soft and tech support.
Oh, and ESP module quite literally doesn't need anything more than a 3.3V power and maybe 2 capacitors to work.
There are a lot of competitors in China, the BK7258 is arguably better than S3, but cost similar.
And if you are willing to sign NDA, there are much better offer from BES.
What BES chip are you referring to?