There is a way to deal with this which can satisfy all parties, but it needs more radical thinking than most pilots are currently prepared to contemplate. Readers will think I am flogging a dead hobby-horse but here goes....
We are talking about maintaining (and to an increasing extent, initially acquiring) basic aircraft manoeuvring skills, in a world where those in charge of operations believe automation is capable of doing this manoeuvring more consistently and efficiently than the human pilots. They prefer to regard crew members as system operators whose presence is primarily concerned with economic efficiency and satisfying regulatory needs. They write rules and procedures for crews to deal with what they BELIEVE are the most demanding circumstances - even if in reality they are not.
If one thinks that way, then basic manual flying skills become a low priority, because for what THEY consider to be demanding situations, the automation is required to be used anyway. This is despite the fact that automation CAN'T actually solve all problems and may actually create an even more demanding situation by dumping a problem back into an unprepared crew's hands, as John T just said. This is belatedly being recognised by some of those at the top.
From the currently prevailing perspective, it is a "given" that automation reduces pilot workload and improves efficiency. So it follows that deliberately using less than maximum automation is unacceptable, because it adds to the workload of the PF. Normally the PF is also responsible for the overall management of the flight which must be a higher priority. With manual flying on instruments especially, the less it is practised, the more concentration it requires on very short term inputs and responses, which must divert attention from overall situational awareness and "flight management". It's a vicious circle and inevitably, managements increasingly regard it as unacceptable, especially if the PF in question may be an inexperienced F/O, or if it is done merely for personal satisfaction.
But IF pilots themselves are also willing to be open-minded, this "automation must always be used because it's needed in our limiting cases" attitude is vulnerable to two facts. These are (1) there is also a second pilot (PM), and (2) the vast majority of the time conditions are NOT close to "limits".
The fundamental objection to manual practice is that it diverts PF's mental resources from the more important overall management task. But if you can make the philosophical leap that it's not necessary for the PF simultaneously to have overall responsibility for management, that doesn't matter. The PM's basic workload isn't much affected by whether or not the automatics are being used. Some readers will recognise where I am going with this......!
Although it will be heresy to most, if you routinely separate overall management responsibility from aircraft handling, it is easy to make manual practice in appropriate conditions entirely consistent with getting maximum benefit from automation when needed. Leaving aside all other aspects, routinely using a pilot-in-charge monitored approach procedure would make it much more acceptable to practice manual flying, and especially it opens up the route to more rapid acquisition of skills by low experience pilots. As others have said, it's largely to do with risk management and desired outcomes. Instead of an "all or nothing" situation - give the leg away or not - as a Captain you can have much more control of how much freedom you are giving an F/O to learn and practice.
While many people are horrified by the idea of a 20 year old with 225 hours, a CPL and an IR, being in the right seat of the latest, most sophisticated aircraft in high density short sector operations, let alone with an ex-military Captain who has never heard of CRM, that was exactly my initial situation over 50 years ago. The "delegated flying" used by my operator then resulted in cadets like me building at least that element of their experience extremely rapidly.
Line flying became effectively an extension of training, as Captains who had no formal training responsibility were supervising this learning and experience building process, using their own discretion as to how much freedom they allowed us to dispense with autopilot, flight director etc. on any individual occasion. But it has to be seen as an entire package of procedures, limits and recommendations.
There is a very informal discussion going on elsewhere among a group of experienced pilots including former manufacturers test pilots and instructors, to try and evaluate a "best practice" recommendation that covers this. I'm open to making the current version available for comment if there's a desire to see it and discuss it seriously, but not if it is just going to get "flamed" as would happen in Rumours and News. JT, as moderator what do you think?