Your question reminds me of Prof. Tao's description of his own tensor power trick. Although sounding as an indirect answer, it might be useful to show the POV of a an exceptional mathematician (and profound thinker) about a topic he masterly treated. Verbatim from here: The amplification trick is a deceptively simple one, but it can become particularly powerful when one is arbitraging an unintuitive symmetry, such as symmetry under tensor powers. Indeed, the “tensor power trick”, which can eliminate constants and even logarithms in an almost magical manner, can lead to some interesting proofs of sharp inequalities, which are difficult to establish by more direct means.

Your question reminds me of Prof. Tao's description of the tensor power trick. Although sounding as an indirect answer, it might be useful to show the POV of a an exceptional mathematician (and profound thinker) about a topic he masterly treated. Verbatim from here: The amplification trick is a deceptively simple one, but it can become particularly powerful when one is arbitraging an unintuitive symmetry, such as symmetry under tensor powers. Indeed, the “tensor power trick”, which can eliminate constants and even logarithms in an almost magical manner, can lead to some interesting proofs of sharp inequalities, which are difficult to establish by more direct means.