On the website for a Chrome extension I sell, 90% of my support requests (mostly from paid users) come in through the chat widget. The low latency communication compared to email means I can solve support requests faster, with less effort on both sides and the sender ends up happier at the end.
Having to receive, read, write, wait etc. over several emails is really painful and sucks up time on both sides even for simple problems and especially for complex problems. It can take several emails to understand a simple problem because most users aren't that precise e.g. "I upgraded but I can't access the paid features". I'm considering pushing all users to use the chat widget by default for support queries because of this.
I wouldn't be against using some chat bot automation either (which people also complain about) to deal with common requests for the initial request message because it's really hard to 100% eliminate FAQs being asked. Especially if you're a solo founder, you want time savers like this.