This discussion is conflating two related, but different, skills that pilots need in order to be successful. You have to understand and consider the two skills separately (and understand how they relate to each other, too).
Stick-and-rudder is the first of 'em, although I like to call those "monkey skills" because they are the fine and gross motor skills that a well-trained primate could acquire. The monkey skills are generally aircraft-specific and require aircraft-specific training to achieve. Sometimes these skills are portable between similar aircraft, but between different aircraft types they are only portable in a general sense. This is why being able to stick that power-off 180 in a 172 doesn't mean you'll also be able to handle the LAX Approach "chop and drop" over Santa Monica in an 80,000# regional airliner without specific training. It is also why veteran airline pilots with thousands of hours moving heavies across the NAT can't just go jump in a P-51 and race it at Reno with any expectation of safety or success.
The second is airmanship, that amalgam of judgment, experience, and decisionmaking (the Navy calls this "headwork", the FAA calls it ADM) which is portable between aircraft and sectors of the aviation industry. Airmanship is the "stick and rudder" of the brain. Unfortunately, this is not a skill that can be taught in a classroom, it can only be acquired through experience (in the USAF fighter community, they like to say "SA cannot be taught, only graded"). CFIs, instructors, and mentors can model good airmanship for their students, and can critique it, but it is ultimately up to the individual airman to actually acquire it and learn to use it. This is a pilot's most valuable skill, and the one which is hardest (and takes the most time) to acquire. A wide variety of aviation experiences (both good and bad) is the only way to develop robust airmanship. It is both the source of a pilot's overall skill as an airman, and simultaneously his Achilles heel (since we know statistically pilot error and bad judgment are the source of the overwhelming majority of aviation accidents)
So, bearing this in mind, in this situation you have to look at which jobs best build each type of skill here. Yes, ideally you'd like both...but those jobs are rare, and most flying jobs are weighted toward one end or the other. Some jobs may build crack stick-and-rudder skills but be so repetitive and limited in scope that they don't build particularly good airmanship. Other jobs could be the opposite, exposing pilots to many different types of operating environments, weather, complex decisionmaking, leadership, etc which builds great airmanship, but are limited or repetitive in opportunities to polish or improve hand-flying skills.
A 121 airline training program expects trainees to need to learn the "monkey skills" of their company procedures and operating their aircraft. They do not have the ability or time to teach airmanship to trainees.
