Which “people” does it lead to a very shallow view of God? Are you talking about everyday churchgoers who don’t have much theological education, and naively take the word “person” to mean what it means in everyday conversation nowadays? Well, yes, they might be misled. But the Greek-educated thinkers who introduced the language of “persons” into the discussion of the nature of God had a great deal of theological education, and they were not using the term “person” as a bus driver in a modern Baptist church might use the term, but as a technical term.
All you have to do is read the original sources – the discussions of the Trinity in the Eastern and Western Fathers (have you read any of those original sources, by the way?) – to see that their understanding of “God” is anything but “shallow”. It’s in fact a much deeper and more complex understanding of God than is held by typical American free-church Protestants. But if you don’t take the time to understand how they use technical terms like “person” and “substance”, you won’t see just how deep and complex it is.
The YECs here can speak for themselves, but regarding ID, ID is not and does not pretend to be a Christian theology, and it has no responsibility to articulate a deep and thorough concept of God. That is a job for the churches and the theologians. ID investigates only one facet of God – and even then, only indirectly, since it doesn’t directly address “God” – God’s mind or plan as revealed in the structures of the natural world.
I suspect that underlying your remarks is some notion that describing God as a “person” makes God into an anthropomorphic or “mythological” deity such as Zeus, whereas God is beyond such limitations. And of course all Christians agree that God is not merely another version of Zeus, but something much deeper. But the very Trinitarian theologians you are criticizing certainly did not hold to a “mythological” conception of God, and did not think of him as just a super-Zeus. Nor do ID proponents – most of whom who are Christian, and quite often very orthodox members of their various denominations – think that God is nothing but a super-Zeus, or that his being or activity is exhausted in designing the world. Your objections seem to be based on a misunderstanding of what the Early Church Fathers were trying to do, and of what ID is about.
Daniel Ang, though a physicist by training, seems to have acquired a good understanding of classical Christian theology, and as someone trained in the history of Christian thought myself, I can recommend his comments as worthy of further thought and study on your part. There are also innumerable good books on early Church doctrine, the Trinity, etc., written by scholars of Orthodox, Catholic, Anglican, Reformed, etc. persuasion, which comment on the Fathers and the development of Christian doctrine on this subject. If you want references to some works I have found helpful, I can give you some.