IANAL, but this is my understanding.
What's the consideration in the written offer? Promises aren't enforceable in court. For a contract to be enforceable, it has to be an exchange of something, not a one sided offer.
https://www.law.cornell.edu/wex/consideration
There are substitutes for consideration. Search for "detrimental reliance" and "promissory estoppel" if you want to go down that rabbit hole.
There are substitutes for consideration. Search for "detrimental reliance" and "promissory estoppel" if you want to go down that rabbit hole.