Actually, there is, in the general case. Ideally, you’d like to establish the equivalence between the absence of arbitrage opportunities and the existence of an equivalent martingale measure, as well as the equivalence between complete markets and the uniqueness of said martingale measure (for a given numeraire asset). That turned out to be a lot harder than some very smart people thought back in the 80’s.
So to be clear, are you saying that it is possible to prove the following statement?
(3) E[ST] = Sert
I don’t think you are saying that, but just asking.
[EDIT] Again, to be clear, I am not denying that (3) is true if we use the risk-neutral expectation operator. Then it is trivially true, for it states that in a world without risk premia, the expected return is the risk free rate. But (3) above doesn't state that. It states that it is unconditionally
true that the expected return is the risk free rate. Which is false.