The sentence is from an old folk tale.
Is the construction in bold suitable only for the folk tale style? It means "I want you to be...", doesn't it?
Is the construction in bold suitable only for the folk tale style?
No. Only the sentence-ender 「じゃ」 has anything to do with stories. The rest of the part in bold is just very normal.
As discussed in this Q&A, 「じゃ」 is a common sentence-ending used by older characters in stories. It is role language that means the same thing as 「だ」 in Standard Japanese.
「[Noun] + を + してほしい」
"I want you to do [Noun]"
When the noun denotes a position or role as in the sentence in question, it means:
"I want you to be/become a/the [Noun]"
「ものだ」 as discussed here, expresses an exclamatory declaration in this context.
"I really would like you/someone to be the young lord's playmate!"