No matter how you twist things, you don't have to be able to procreate in order to marry.<quoted text>
Actually, YOU left out the first logical step.
In reality, marriage always has included the likelihood of procreation. So much so that the instances where it did not occur were ignored.
Moreover, you then simply argue tradition, without a valid reason to discriminate.
The only reason marriage was restricted to one man and one woman, was the very issue of procreation.
By removing that element, you leave the setting of a natural family undefined, horn in on the protection and support designed for that foundational societal relationship, and open the door to simply any committed relationships. ANY restrictions of number and type must show harm, and children cannot be considered.
The whole logic thing, beyond you, huh?