How does cid make power?

The thought on this site is generally a similarly built engine of different displacements the larger one will make more hp, so you have to at least build similar equipt engines to compare.

Your logic in this endeavor has been wildly inconsistent.

The question was does CID make horsepower. The answer is absolutely.
The secondary question is whether a comparable engine with more CID will make more HP, and the answer is still absolutely.
The tertiary questions is whether the larger engine will make more PEAK HP, and that's a lot more complex because flow will dictate the rpm range for both, and the answer would depend on WHAT RPM you want the power compared at.
The quaternary question is whether it makes financial sense to increase the CID for more power, and the answer is again complex. If you have a bad-*** top end, then yes - make more CID. If your 273 peaks at 4500 rpm, you probably need to open your wallet for a better set of heads first.

There is no blanket answer for whether CID makes HP in ALL cases because that game is too easy to rig. At what RPM? What is the goal? Where is the torque needed?

A bigger bore wins in every case, but that's physically constrained by the engine design (bore centers). Stroke is the only other way to increase CID once bore is maxed out - but the question isn't about stroking vs boring, it's CID vs CID - and in general more is better unless there's other factors crippling the performance already. If the CID of a PERFORMANCE engine is increased and power doesn't increase, then something else (tight wallet) is holding the engine back - not the CID.