The problem with your argument is it assumes that CBMM is always unfair and SBMM is always fair, when they're not.
"Fairness" is not only determined by Relative Skill but also by other factors such as lag and hit-registration. It's not fair for two equally skilled players to shoot eachother in the exact same way and have one of them rewarded and the other punished due to lag.
CBMM can result in low-skill players being match-made vs other low-skill players, or it can sometimes match make them with higher-skill players, it's Random.
SBMM on the other hand may not always result in laggy games with poor hit-registration, but it does so at a higher degree than CBMM does.
You can't sacrifice the "connection-based" component of "fairness" in order to satisfy the "Equal Relative Skill" component of "fairness" you defined.
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100% agree. Fairness is more than just skill. CBMM is the most fair because everyone has an equal chance. What you do with the chance is up to you.