Describe your design idea/issue

cirq.ControlledGate(cirq.Z) decomposes to

S(q(0))
Z**1.5(q(1))
(0.7071067811865476+0.7071067811865475j)
Y**-0.5(q(1))
CZ(q(0), q(1))
Y**0.5(q(1))
Z**1.5(q(1))
(0.7071067811865476+0.7071067811865475j)
Y**-0.5(q(1))
CZ(q(0), q(1))
Y**0.5(q(1))
Z(q(1))
-1j

Of course, it is equivalent to CZ and should decompose to CZ.

In ControlledGate._decompose_ it probably makes sense first to try canonicalizing itself, and returning that if there's a canonical form of itself. Something like if self.subgate.controlled(self.controls) != self: return [self.subgate.controlled(self.controls)]. This would allow getting rid of all the cruft from the CZ example above, and there are other cases that would benefit from this approach too. In particular, combined with #7241 and #7238 this would allow getting rid of all the special handling for CZPowGate in ControlledGate._decompose_.

This is a pretty straightforward change, I believe it only requires adding the above logic to ControlledGate._decompose_ and a couple unit tests. Marking as good first issue.