Why/when is である required for na-adjectives in grammar forms?

Question

When shin kanzen master defines the connections for some grammar forms, it often notes that である must be used for na-adjectives.

For example, in the grammar point for ～にもかかわらず in shin kanzen master grammar N2, the following connection rule is given:

名・普通形（ナ形 だ - である・名 だ - である）　＋にもかかわらず

It seems this connection rule needs to be memorized to get the correct answer to exercises.

For example, exercise 10 on page 127 of shin kanzen master grammar N2 states:

（　　）の中の言葉を適当な形にして、必要なら「の」を加えて＿＿＿の上に書きなさい。

...

10　この本は、内容が非常に ＿＿＿＿ にもかかわらず、よく整理されていてわかりやすい。

(複雑な）

The solution for this exercise is 複雑である. In particular, the addition of である is necessary to satisfy the connection rule given in the grammar point's definition (as written above.)

There are many other grammar forms that require である for na-adjectives. Rather than naively memorizing all of these cases, are there general rules to know why/when である needs to be used to connect a na-adjective to a grammar form?

Answer 1

There are rules, but they are complicated.

The short explanation:
1. にもかかわらず needs to be preceded by a noun or noun equivalent.
2. a noun equivalent can be made with a nominalizer.
3. in the case of にもかかわらず the nominalizer の can often be omitted.
4. the nominalizer needs to be preceded by 連体形.
5. だ is not 連体形, it is 終止形, so it needs to be replaced by a 連体形 such as である.

The longer explanation:
Anything that can be conjugated in Japanese is called 用言.
There are 3 kinds of 用言:
動詞: verbs
形容詞: i-adjectives
形容動詞: na-adjectives

There are 5 conjugations:
未然形
連用形
終止形: used at the end of the sentence
連体形: used before a noun
仮定形: to express condition
命令形: to express order

The site below shows how to conjugate na-adjectives:
https://www.kokugobunpou.com/用言/形容動詞-2-活用/
きれい だろ う　　（未然形）
きれい だっ た　　（連用形）
きれい で ない　　（連用形）
きれい に なる　　（連用形）
きれい だ 。　　　（終止形）
きれい な とき　　（連体形）
きれい なら （ば）（仮定形）

So let's go back to the explanation above:

1. にもかかわらず needs to be preceded by a noun or noun equivalent.
   Examples:
   学生にもかかわらず
   先生にもかかわらず
   

2. a noun equivalent can be made with a nominalizer.
   Examples:
   書くのにもかかわらず
   飲むのにもかかわらず
   

3. in the case of にもかかわらず the nominalizer の can often be omitted.
   Examples:
   書くにもかかわらず
   飲むにもかかわらず
   

4. the nominalizer needs to be preceded by 連体形.
   Examples:
   書く(の)にもかかわらず
   つまらない(の)にもかかわらず
   元気な(の)にもかかわらず
   

5. だ is not 連体形, it is 終止形, so it needs to be replaced by a 連体形 such as である.
   元気である(の)にもかかわらず
   Wrong: 元気だ(の)にもかかわらず