The marketing and sales departments never targeted the editorial/dev team of a website/company but directly the sales department or an upper management department of the potential new customer.
Chances are that the developers of those websites have to suffer those bullshit integrations as much as you do. And they also are asked to integrate them.
Funny story: at my previous job the widgets were disabled "forever" from the site (via a cookie) once you logged with your company email. Marketing and marketing devs had emails in another domain to test their widgets.
I used the chat solution of my broadband provider just a couple of weeks ago and it was a really good experience.
Also, as a former support technician I far prefer text from both sides of the table.
That the customer may not be satisfied afterwards doesn't matter - there are plenty of mitigation strategies, such as lock-in effects, playing off sunk cost fallacy, or drowning negative feedback on third-party sites with bought ratings, reviews and social media likes.
Seeing a site like this should light an immediate warning site in your head, telling you that you don't want to be on the business end of their business goals.
The business just provided the most value™ to the customer at that moment in time
That being said, the value that these patterns are gaining the businesses that employ them, must outweigh the value lost from people who are so annoyed that they take their business elsewhere.
It is how it is, unfortunately.
I removed it mostly because it takes a lot of effort to maintain a good level of responsiveness on these kind of things unless you have a dedicated support team.
Some of these support chat popups are a bit too in-your-face, but it sure beats hunting down some email address somewhere.
Ridiculous.