Kudos for attacking a problem many people would consider “solved” or a “saturated market.” It’s never a bad idea to incrementally improve on existing products.
However, looking at the market for these products I could imagine a freemium model where we might charge for some extra features (chat app on phone, customization of chat widget).
I strongly believe customers should experience the magic (wha! someone just started chatting with me and now has a nice, personal experience) first and freely.
Distribution, as so often, is probably going to be the challenging part if we really want to turn this into a business. We should maybe focus on some kind of niche where such a product is currently not used or not used often. Ideas welcome :)