Maybe there is a way to utilize the website owner to bootstrap the chicken and egg problem.
So i'm assuming 'Customer Messaging on a website without website owner's action' would be a browser extension? If so, what if you made the pitch to website owners that if they signup and just embed your chat on their site, then they are allowed to moderate the content. Otherwise, users that have the extension will be able to just chat about the website owners products without moderation.
Once you get embedded on a bunch of websites, then you can offer an upgrade path for those users to get the extension and chat on any website.
OP of that need gap explicitly cited Amazon, chatting with amazon customers when buying a product instead of relying upon reviews which are often fake.
Sites like Amazon wouldn't bother to enable such provision and hence the need for 'without owner's action'.
Right, but imagine the product would work on any website and you got a bunch of users (by bootstrapping with those website owners). Now those users can visit amazon and chat with each other because they have the extension installed.
Basically, imagine if Honey added realtime chat between users who were on the same website. That would solve OP's need. Question becomes how do you get the install base of Honey? If I had to do it, I'd try to get website owners to embed my chat and have the embed promo users to download the extension.
So i'm assuming 'Customer Messaging on a website without website owner's action' would be a browser extension? If so, what if you made the pitch to website owners that if they signup and just embed your chat on their site, then they are allowed to moderate the content. Otherwise, users that have the extension will be able to just chat about the website owners products without moderation.
Once you get embedded on a bunch of websites, then you can offer an upgrade path for those users to get the extension and chat on any website.
Just an idea!