TL:DR; We set out to have a no-cookie homepage. Replaced Google Analytics, Crisp Chat and Cloudflare with privacy friendly alternatives!
For the homepage I'd say visitors message rarely so it is less useful. That said, the ones that do are usually the same who convert as they are already fairly qualified leads and just want a little extra info before they sign up.
One - the person on the other end works for a different company and they can answer a few common questions, but everything else is "call this 800 number." Cell phone companies do this.
Two - the person immediately says "give me your phone number and lets talk on the phone" (car dealers are terrible for this).
I guess there is a third type - companies using a laughably terrible bot. I encountered this with Sony after I bought a game online and it wouldn't start. I eventually called in and they instantly refunded my money because I think it was a common problem.
This is a common yet naive thing to say that is rarely ever true in practice.
The retargeting most of us are see is the failed kind where you’re trying to sell a fridge to the person who already ordered one two days ago, and you’re the person who sold it, but your retargeting partner does actually support registering a purchases.
I’ve paid close attention over the past few years and have found >80% of the retargeted ads are for something I just purchased (and they are usually the “single purchase” type product, similar to the fridge analogy you used)
Even if a big share of your ad impressions falsely target someone who already bought (see sibling comment) the remaining impressions lead to an increase in conversions at a comparatively low cost per conversion.
As you said, this will vary from business to business, but I have seen very successful retargeting campaigns in b2c e-commerce as well as b2b lead generation.