I think part of the appeal of thumbies is simplicity and the other is pure aesthetic. While most shifters now work well most of the time, there is something about the fact that I can take thumbies apart completely and rebuild/repair them that I like, and on low number cogs like 5-7 or 9 they work good. I also like being able to feather the chainrings. But, I also have two bikes with integrated shifters as you have and like them as well so I could not say one is objectively any better than the other - just depends on what you like. Another point is that with thumbies you can move them independent of the brake to put them wherever you want.

The aesthetic is harder to justify objectively. Some people just like the old school look/function and are even willing to pay a premium for it. My integrated shifters (like yours) did in fact cost about $55 CAD but I have also bought cheap functional thumbies for $15 (though new retros are definitely more expensive). The good thing is, if you can find an old mtb junker the all metal thumbies can be cleaned up and will work just as well as day one. They really will last forever.

I also sometimes ride in the position you indicate but rest my hand over the brake/shifter lever for a wide relaxing grip. In looking at the crazy bar pic I have already said the grip surfaces are way too large. You could reduce the cruiser grip position easily and slide the shifters down, giving the needed room for that cross bar position. Or you could put them inboard near the stem, or at the base of the barend/aero bars. As said, the thumbies allow you to position them independent of the brake.

There is no right or wrong. I would give a bit of weight for ease of use to well adjusted integrated shifters, weight to the thumbies for simplicity, weight to them as well for aesthetic but only at a penalty for cost (if buying expensive retro new ones). I could not argue but a draw either way for basic function.