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?
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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!"