I suspect it depends how you understand the Trinity doctrine and the sense of "persons" in the first place.
If your view borders on tritheism ("three individuals of the 'God' species" out there) there is indeed no reason why you should not relate to the three in the same way. But I don't see any reason why there should be 3 instead of 2 or 4 or 10,000 either.
If, more classically, your Trinity is understood as one God unfolding in three "positions" or "roles" (hupostaseis or personae) -- above us (the Father), with or before us (the Son) and within us (the Holy Spirit), structuring a symbolic space, then the question of prayer appears in a different light. And then prayer is naturally to the Father through the Son by the Spirit -- according to the overwhelmingly majoritary practice of the Christian church from the NT onward.
One argument sounds particularly weak to me:
26] Likewise the Spirit also helpeth our infirmities: for we know not what we should pray for as we ought: but the Spirit itself maketh intercession for us with groanings which cannot be uttered.  And he that searcheth the hearts knoweth what is the mind of the Spirit, because he maketh intercession for the saints according to the will of God. - Romans 8:26:27
How can the Holy Spirit make intercession for us if He is not a person?How can he know us if we fail to speak to him? For such close intimacy, we must have an interaction with the Holy Spirit that reflects communication, love, understanding, and a sharing even of our most secret feelings that cannot be uttered (spoken outloud.)
If the problem is that we don't know what we should pray, how would it be solved by changing whom we pray to? Paul's answer is, the Spirit intercedes because it (or he, or she) knows already what we feel and need and can express it (which we cannot) -- or, in Trinitarian speak, because it (or he, or she) is within us and he is God.
Praying tothe Holy Spirit is actually putting it/him/her out of ourselves, and, imo, missing on the deepest "logic" of the Trinitarian dogma.
(A very disinterested remark, fwiw.)