I used to have one on my contact page. In total I got 2 chats in the time I received 50+ emails. Totally not worth it, especially as for one chat I couldnt even reply before the user abandoned the page.

I use them for support for various SaaS I manage at work. Really convenient for that. Use one or another maybe once every 2 or 3 months. I don't think I've ever used one on a site where I wasn't logged in, though.

I could maybe see using one on a pricing page or something like that, if I couldn't figure out which plan was what I needed.

We have one in our app, I've been amazed how users have reported so many bugs, feature requests, and tiny issues through it. Chat widget was totally worth it.

If you have traffic, yes. I get hundreds of chats per day using the chat widget, some for support, some for pre-sales inquiries.