At different times, the surrounding copy was something like “Question? Suggestion? We’re at your service.” or “How can we improve this page? We’d love to know.”
It worked great and I’d do it again for any new app. People brought up issues large and small. The goal wasn’t to “engage” or “nurture” or whatever. We just wanted to respect visitors’ time, which meant being as easy to reach as possible.
I see now they put some more "unlock to get" things on their website but still their free offering is good enough. The only limit is after 20 live chats you get emails instead.
For us we use it mostly for getting the initial question (in offline mode) and then we take it further via email.
Also: how about a feedback@ or support@ email address, and link to it on your webpage? (The form mentioned above can work by sending email to this address, even, so everything goes to the same place.)
RFC 2142 defines "webmaster@" (alias: "www@") as the standard email contact. I think it was a good idea, but I don't know how common it is any more.
I like to report bugs whenever I find them, but it's surprisingly difficult to find any sort of feedback mechanism for most webpages. Half the time, "tweet sarcastically in frustration" is actually the best option.
They offer Freshdesk for a customer support portal/ticketing system, and Freshchat for live chat. Total cost is a fraction of what you’d pay for Intercom, and the products are continuously adding new features.