Is shear stress in the tensile test of low-carbon steel a controlling factor? Why?

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The book states that when low-carbon steel is stretched, the shear stress is greatest at a 45° inclined plane; upon reaching yield, 45° slip lines appear on the surface, and the misalignment of the inclined sections leads to slip, which prevents an increase in stress while strain continues to increase. I’m a bit confused: does yield caused by shearing occur before yield caused by tension? Or is the controlling factor the shear stress in the 45° direction? According to the book, for a 45° inclined surface τ=σ/2, which is only half of the axial tensile stress, it yields first. In fact, even for low-carbon steel (let alone high-strength steel), it is 0.6~0.8, which is much larger than 0.5. It seems that when the critical tensile stress is reached, the critical shear stress has not yet been attained; then why do books or experiments suggest that shear yield occurs first? Is my understanding correct? When low-carbon steel is stretched until fracture occurs, necking takes place, and the fracture surface is essentially flat. Since yield failure occurs first, wouldn’t it be easier to understand if the material simply broke along a 45° inclined plane instead of forming a fracture surface? Then, stretch yield must have also occurred during this process; how can we determine that it was the 45° shear that caused the stretch yield rather than the tensile stress at a 90° interface? Maybe my question is rather stupid; I hope experts will kindly offer their guidance. Thank you very much