Not, if the runtime for calculating a sig is dependent on the number of bits of the payload.

It is a common misconception that basic operations are in O(1), but that's wrong. Even addition and multiplication of larger numbers take longer than of smaller numbers. The same hodls for sig function.

I like the conceptual idea of having set-based transactions because set-based thinking is one of the principle of modern computer science.

What I was trying to explain to you was that you should not make not unproven statements.
Show me the runtime complexity of the sig function in terms of payload length and we'll see.