For one thing it is a further evidence of the Spirit's personhood, and supports the idea of the Trinity. I don't see it as any big deal that the Spirit "took" or "led" Jesus into the desert. Jesus also prayed to the Father. We know the relationships. The Spirit leads US, and we are to pray to the Father.
My point was that God is never partially God, but always perfect, complete God. This is suggestively implied, in my opinion, in Mat 3:16, where the Holy Spirit is seen descending on Jesus after he emerges from the baptismal waters.
Christ's divine nature is complete, perfect God whis at no time without the Father or the Spirit.
In Mat 4:1 it says that fllowing His paritsm and the HS descending on Him, Jesus was ledleading and Jesus following to be tempted of the devil.
Why would He be led by none other than the HS to be tempted? First, I propose that the Word was with the Spirit all the time, and with the Father, and that He didn't need to be led by anyone as if lacking in ability to lead himself, why the temptation when God knew that it would not work.