Unorthodox Door?

I wanted to sheet 2 old solid wood doors with 1" X 6" T&G pre-finished cedar because the doors have sagged over the years & have numerous coats of paint which I don't want to remove. But this will leave me with very thick, >3" & heavy doors. So I thought about building a mortise & tenon frame & sheeting that, but it's still going to make it thick & it could twist as dimensional lumber isn't that dry. So I thought , what about a sheet of 1/2" ply with the T&G attached to both side?
Don't think I 'I've heard of this before, so I'm wondering what the drawbacks might be? Shouldn't sag too fast, shouldn't twist. Any thoughts ?
Thx, Chris
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