Pro- the SSD will live longer
Con- the RAM will fill up more, especially when opening resource-heavy pages (though there's a way to unload inactive tabs so that might not be that big of a deal, and especially if you have enough RAM to spare)

Personally I've been using memory-only cache for about a decade (half on HDD, half on SSD) and I don't think I've noticed any adverse effects from that. (though I rarely have more than 5 tabs open at once)