Thus there's nothing gained from hardware, so claiming there is a constraint on software that is not in hardware isn't really correct. Both have the same constraints for fixed size machines, and both allow fast solution for unbounded size machines.

There's plenty of such "other machines" that solve NP hard problems in P time, such as closed timelike curves, chaos machines, infinitely precise engineering, etc., but such machines are generally not physically realizable, and most are not even cost effective for small n, so people use complexity to mean how the problem scales on physically realizable, cost effective devices.

If every conversation about complexity had to go through this same digression to clarify that there are indeed other areas of thought about computation that have different conclusions, then no one could cover the original topic.

Currently the Church–Turing–Deutsch principle seems to be the best formulation of such issues, and Deutsch added the physically realizable part to remove from consideration things that are math but not physics, since such machine concepts are not useful to do actual computation.

All good stuff :)