It appears in Google, but I don't think "written in stone" would be a good substitute verb for this particular expression. It could be that people say, "It's not carved in stone" to mean "It's not permanent" or "It's not been decided yet".
"written in stone" - Google Search
We could say written in ink. But if we say "written in stone", I might think there's a such thing as "liquid stone'.
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