This is currently possible with Hackintoshes, but only because Apple tolerates plausible-but-fake serial numbers that follow their usual format. They can trivially restrict this if they want to.

Couldn't I go to the Apple store & copy down a real serial number?

Let's not endorse committing fraud here. (Also, such activity could harm innocent purchasers of devices with stolen serial numbers.)

It's an interesting thought experiment though.

Who is harming the purchasers? Apple, or the hacker copying down a publicly available piece of information?

Easy; it's the hacker. Whether the false information is publicly available is not a defense to fraud. Fraud is presenting false information (public or not) as true (in this case, that the serial number of the item belongs to you as a bona fide purchaser) and an innocent party (Apple + the consumer) relying on it to their detriment.

A serial number is not a password, it's a username, and copying it down isn't hacking.

Copying it down isn't the problem. Falsely claiming that it is associated with a machine that belongs to you is.

Tying an app to hardware identifiers (effectively dongle-based DRM) is the problem.

I vote that serial number information would hands-down not be considered a "publicly available piece of information" in court.

Serial numbers are generally used to corroborate ownership of an item in legal scenarios (and may count as a conditional representation of PII).

Apple uses them as unique identifiers to authenticate their devices and tell them apart, and very presumably protect against various forms of fraud.

Where SecureROM is up there in terms of being buried pretty deeply in the SoC, I imagine the serial number is on a similar level in terms of not being modifiable/forgeable. So the "device <-> serial number" relationship is pretty indelible, you can't change it. And given that the way the relationship works is that you buy the hardware and then it becomes your property, you also effectively "own" that serial number to a relatively concrete extent. Thus, I can see slapping a theft charge on someone who runs off with the serial number of a device they did not own.

There's probably a much more concise way to wrap up the "nope" - the above points are somewhat general - but TL;DR, I really don't think that would work.

The public-information question isn't even an issue that a court would consider in a fraud allegation. (We're not talking about theft of trade secrets here.) It's a red herring and isn't worth the effort to discuss.

Exactly; the Hackintosh community explicitly provides instructions on how to ensure the serial number you generate is not another real Mac’s serial number, but is “valid” for the model you need to emulate for your hardware.

Otherwise this could cause issues with a real owner or the Hackintosh community, and is just acting in bad faith.

Yes you can, however there's a good chance it may also carry over the iCloud Activation Lock status and refuse to work for that reason (all Apple Store machines are Activation Locked to deter theft & assist with recovery).

This might get you in trouble though, less about the theoretical element of fraud and more that they’ll legitimately believe the device has been stolen.