大辞泉 lists どんな as 形動=na-adjective, according to which どんなだった is a totally grammatical plain usage.
For the particular case, どんな人だった sounds like referring to the personality (the person was gentle or nasty or whatever) and どんなだった feels more appropriate when talking about the appearance.
In terms of idiomaticity, I can't give a clear distinction, but as you guessed どんなだった is less common (or less frequently used) than どんな＋Noun or どう.
- How was the travel? 旅行はどうだった (どんなだった is less common)
- What kind of person was he? 彼はどんなひとでしたか
- How was he? (彼はどんなでしたか)
I think the difference between 2/3 in English more or less corresponds to that in Japanese. 2 asks what he was like as a person and 3 about his condition. In some specific contexts, 彼はどんなでしたか can be used (e.g. the asker knows he is ill and asking the person who visited him how ill he was), but in most cases 彼は元気でしたか is more appropriate (just like how are you).