And this means that when everything conjunction-intro requires is true, then the conjunction it allows us to introduce must always be true.
Earlier I asked, Why is using ∧Intro more demanding than using ∨Intro? Now we can see exactly what the answer is.
Speaking entirely formally, we can use whatever rules we like.
But we want our rules to mirror logical validity--given truths, we want them to take us only to truths. We want them never to take us from truth to falsehood.
For this reason, given the truth table for conjunction, ∧Intro has to require that we already have both conjuncts.