A fully developed brain is not necessary for critical thinking and decision making. It may be necessary to solve equations without a pen and paper, for example, but it is not necessary to decide when and with whom to have sex.
It's true that a developing brain can still think critically, but it won't perform at the same level as if it were fully developed. How far along do you believe a brain needs to be developed in order to make decisions regarding sexual consent? Should the brain be capable of performing hypothetical-deductive reasoning? Only concrete reasoning? Where are you drawing the line in regards to development?
I see that Traveler already drew attention to the prefrontal cortex in her quote from NPR, but it's worth going into a bit more detail. The prefrontal part of the brain is THE driving force in sexual motivation and decision making, and during puberty it is underdeveloped.
Look at those keywords again: underdeveloped, sexual, decision making
. That's really all that needs to be said. And post-puberty, the prefrontal cortex is still growing- one of the most notable changes is synaptogenesis
and it's pruning process: trimming synaptic connections and making the cortex more efficient.
So I would say that a fully developed brain is necessary to make the best
decisions concerning sex. With regards to your point about age being irrelevant- it's relevant, primarily because of the developmental reason above.