What am I missing here?

Say you have a hose and you pinch the end. I'm going to absurdly conclude the speed should be the same.

If I have a tank of water and at height 0 I punch a hole of area A, what speed does the water come out at?

By Bernoulli's Principle:
v^2 /2 + gh + p/? = C

Inside the very large tank the speed is 0 and the height is 0, giving us:

p/? = C

Outside the pressure is 0 and the height is 0, giving us:

v^2 /2 = C

Therefore:

v^2= 2 p/?

Which tells us that the speed the fluid comes out has NOTHING to do with the area of the hole.
And therefore pinching a hole in a hose does nothing.

This is obviously wrong. What happened?