I can't defend tumbler. But with regards to turntable vs non-turntable (which if you are unlucky might default to tumbler), I have some ideas. In general I feel more comfortable with turntable mode (and have used it in Blender, game engines, and robotics software). When I started learning CAD I initially switched from the default trackball to turntable as well but after a while I switched back to trackball.

Turntable makes most sense when there is well defined and easily identifiable up direction like when you are working with 3d environments or humanoid models. With mechanical parts that you make in CAD software up direction isn't always as clear, you can easily forget where the up was if you don't pay attention to axis gizmo. Plenty of parts can have critical features on all sides, and the preferred "up" direction in most useful views for the part doesn't necessarily match with the up direction of whole assembly.

Turntable view has one downside which the article didn't mention - lack of "state independence". The behavior of mouse movement depends on the angle from which you looked at the start. This can result in situations where you meant to rotate around one axis but it rotates around different one or the rotation happens in opposite directions. Tumble and trackball don't have this problem as rotation isn't affected by global axis direction.

One more potential factor is use of 3d mice. I haven't used one myself, but I would assume that it somewhat avoids the most confusing aspects of non turntable modes. Thus in the best case reducing the need to improve default behavior for regular mice, in the worst case hacky 3d mice integration depending on the chosen rotation style which might brake if something other than tumbler is chosen (I really hope that no 3d software does this, but I lack the experience to confirm this).

This makes me wonder has any software tried dynamic turntable. That is turntable where the role of z axis is replaced by whichever axis was closer to up at the start of mouse drag. Always one of the 3 axis, not the local rotation up direction.

I love tumbler and never want to go to anything else. After a while your intuition starts to cooperate with what path your hand takes to get desired rotation. I can rotate into any orientation without thinking about it in a single sweep, including how my camera is rolled. Its honestly very powerfull, albeit hard to get used to for the first time.

It really depends on the types of objects you're trying to look at and why. The one thing that the article gets right is that turntable makes sense if the object has a natural Z orientation. Things like buildings, furniture and automobiles are obvious examples. Hand held objects get viewed from all different angles, and tumble (or trackball) makes more sense. Some of those objects may have a typical rest position where there's a natural up orientation (e.g. a computer mouse), but they can easily be rotated and viewed from arbitrary angles.

Any decent CAD system will support both turntable and tumble, defaulting to a user-selected choice, with easy options to override the behavior and switch to the other.

It's definitely harder to learn, but it's way more powerful. CAD is aimed at power users.

That circle trick mentioned elsewhere does make it bearable. Small circles with the mouse reorient it slowly. Large circles reorient quickly. So with the tumbling and the circle trick it can be tamed.

It's more flexible. For example, compare the "Turnable" and "Tumbler" rotations in the article; you will be able to set arbitrary orientations in the latter, but not the former.

More like you are accidentally forced into arbitrary rotations with the tumbler, because of how moves correspond to inconsistent axes depending on the way you're turned.

Honestly I don't see that supposed failing as much of a downside really, because A) most of those extra rotations don't change the camera view in any meaningful way, they just roll it, B) you can typically rotate the object on top of the camera if you really need these rotations, and C) it makes control much more accurate.

I think the "turnable" approach would be fine if it included an extra roll control. Probably preferable due to the ease you point out; this overcomes the limit you point out.

My personal preference, and how I've set up my visualization engine (For chemistry vis projects and similar): Move the camera; not the object. FPV controls, plus a roll axis, with crouch/jump for up/down. Works best with a videogame controller, but FPS standard + Q/E is fine too! Full control, and intuitive if you've played those sorts of games. This is full 6 axis.

See circle trick comments elsewhere or briefed under your top post.

I've been told by texture artists that the Tumbler-style has advantages when projection-painting across a model with a tablet...