Do not think that calculate 1 sig has constant runtime = O(1). It should be depend on the size of the to-be-verified payload.
Huh?
You've lost me - a sig is a sig - that is a one time function over data.
If you have a tx that outputs from X to 1000 other accounts it only requires 1 sig check at the end to verify. That will be basically 1000x faster than having a sig for each of the 1000 accounts.
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.