I can only give my experience of working on the cx phone team and it looked like other areas of the business were much better managed from what I could see.
At first you are made to think this is a lovely team with lots of support but actually the team leaders are not qualified (you'll find that tails.com love to give job titles to people with no experience) and you'll be made to feel inadequate at every 121 meeting. Even when your QA score is above 95% you'll be lucky to get a mention or a well done from your own team leader who seemed to have a big issue with handing out any praise. I even had to let my team leader know that her constant negativity was affecting my mental health but she was unable to change her style of management (due to lack of experience).
When I first started there was a delivery incident which meant customers were calling in and screaming at us, literally every call was abusive and due to so many team members being off sick you struggled to even get a toilet break or take a minute to breathe before the next customer started having a go at you. When a couple of us raised this with the team leader we were told "what do you expect?", there was such a lack of empathy and no communication on how we were expected to handle the calls.
If you decide to take a role in cx then don't ever give any negative feedback as you just get added to a hit list and they make life pretty miserable until you just quit, they then pretend to the rest of your team that you left of your own accord. Every month 1 or 2 team members left and the phone team was quite small (around 12 of us) so you'd think this would be a sign to management that something wasn't quite right but as they don't bother with exit interviews I don't get the impression they care.
You'll only be allowed to move to a different department if you keep your mouth shut and just nod and smile.