What is the difference between でいる and である in this example?

Question

From Bright Side Japan:

現代の女性はなぜ独身でいることを選ぶのか (link here)

1. Is it still grammatical to use である instead of でいる in the above sentence? If not, why not?
2. If it is possible, what is the change in meaning?
3. Can you give other examples which highlight the difference between でいる and である?

Answer 1

1. Yes, 独身である is also grammatical.
2. This でいる has a mild nuance of "to stay/keep ～". である is just a stilted copula (literary version of だ). Using である will change the meaning from "staying unmarried" to "being unmarried".
3. For example,
   • 元気でいます。
     I'm doing well (recently).
   • 元気であります。
     (Aye,) I am fine (now). _{(sounds like a samurai or a soldier)}