If I understand you correctly, you're basically asking two related questions:
1. what is the impact of the Trinity on our prayers; and
2. is the recent trend towards praying simplistically to Jesus a symptom of an unhealthy anti-intellectual anti-creedalism?
Re 1: we pray to the Father, through the Son as our intercessor, in the power of the Holy Spirit. The NT pattern seems to be:
* the Father has priority in planning & willing all good things;
* the Son, in incarnate Jesus Christ, is the one who actually puts all the good things into effect - they are all "in Christ"; and
* the Spirit actually enacts the spiritual blessings in us & for us.
So, when we pray, we reflect this pattern. We pray to the Father, as our heavenly Father. We have become his children in and through Christ - by his death and resurrection for us; and by us putting our faith in him; so that we identify with him, and he with us. Ref: John 5:19-17; John 14:13-18 ; Gal 4:6; Eph 1:3-14; Eph 3:14-19; Col 1:3-14; 1 Pet 1:2.
That said, I don't think it's necessarily sinful to pray to Jesus. Stephen does: Acts 7:59-60. I can't think of any bible passage where someone prays to the Holy Spirit; but, seeing as the Spirit is God, again, I don't think it's sinful to pray to him.
But it is better to follow the Biblical pattern as above. That's because the Christian life is not one of minimum requirement - "what's the least I can do to please God?" - but one of maximum heart devotion - be perfect as our heavenly Father is perfect; all our heart, soul, mind & strength; our bodies as living sacrifices.
And that brings us to 2. Simplistic praying to Jesus may be a symptom of anti-intellectual anti-creedalism - which, I think, is just laziness. Christianity is not merely an intellectual matter. Granted. But it's not un-intellectual either. "Love the Lord your God with all your heart, soul, MIND and strength" (Mark 12:30 & Luke 10:27; Matt 22:37 drops strength but retains mind).
That said, I won't jump on someone & criticise them too harshly for praying to Jesus. The doctrine of the Trinity is a tough one to wrap your mind around. The incarnation is a wonderful truth; Jesus is the one who became human and died for us; so it's easy to feel close to Jesus.
The solution, I suppose, is to emphasise that in Christ, the whole Trinity comes close to us: John 14:6-10, 16, 18, 23. This is why we pray to the Father; because, in Christ, he really is our heavenly Father! Rom 8:15-17; Gal 3:26; 4:6-7. We're part of God's family; we have a sure expectation of living with him in glory forever - it's what makes heaven heavenly. This is an intellectual truth to be understood and assented to - but it's so much more than that: it's a personal, spiritual, theological (in the sense of "God-oriented", not just human-focused) reality, to be enjoyed and rejoiced in.
What do you think? Does that help?