Government agencies get copious amounts of customer service inflow and complaints. Despite GOV.UK doing a great job redesigning government services, there are still a lot of reasons to get in touch. In my case when I got the above message, I had forgotten to deposit a tax refund cheque from 2018 that has now expired and I need reissued. There's no self service for that and thousands, if not millions of other niche queries.
HMRC alone received 50 million phone calls, 2 million webchats and and 12 million letters in the tax year ending in 2017 alone. The DVLA is the biggest employer in South Wales, employing 6,000 people in Swansea. They get 27 million calls a year.
The above screenshot I saw today when trying to use the HMRC webchat option is something customer service teams should never do. I would have rather be put in a queue even if it tells me it's going to be hours than have no certainty on whether I will even be able to get in touch.
They're not doing their customer service team any favours either. Not allowing customers to get through means their customer service team is getting bad data on how many people are trying to get in touch with them, so have no true idea of how to properly staff their teams to meet inflow. Finally, what ends up happening is they reroute their customers from trying to use chat, which can be very efficient as agents can handle multiple chats at a time, to calling in on the phone, putting more pressure on their already overwhelmed call center, where an agent can only handle one call at a time.