Hold on. If you go to that question and read OP's comment to my answer, you'll see that this was a fraud by a house-sitter gaining physical access to their book of checks. (And that is why I use a PMB). So your proposal wouldn't have helped at all in that case.
Your idea removes "well-understood" and creates "opaque".
You're essentially talking about the check numbers being a one-time pad, which only the bank knows. So only the bank could attest to the validity of a particular paper check. (This also puts third party check printers right out of business, but nevermind that).
Well hold on. The bank already knows your check numbers. They know them because they cashed your last one, and can add +1. So can you. And most people who have any care with their paper checks, reorder checks so the numbers are sequential to the checks they already have - in fact third party check printers need to know which number to start at.
So if you just wrote 4361, the bank won't be surprised by 4362 or 4366 (as long as 4362-5 arrive soon after)... however if a "1003" shows up, it's pretty easy to automate the task of presenting an image of checks 4361 and 1003 to see if their handwriting and signatures reasonably match. If 100 of these instances happen a day, and an auditor can compare signatures in 2 seconds, then you're talking about 5 minutes of an auditor's time to screen the 100 cases and escalate the 3 faulty ones.
What your trick does is close one gap: where a fraudster knows your last check number and issues new cheques reasonably close in number. However, that was never that much of a gap: it's arguably a feature, not a bug.
- If the fraudster issues checks sequential to the known number, they'll collide with real checks the account holder has written. That's a lose-lose for the fraudster: even if the fraud check arrives first, it means the legitimate check bounces, and the payee alerts the account holder! Quick attention is the enemy of fraudsters, they need the transaction to go unnoticed for weeks so it can't be quickly reversed among the banks. That's especially true if they're using a "patsy" to receive the money.
- Any near-number check fraud has another fatal flaw: near checks are supposed to be similar in appearance. But the fraudster's won't be. Remember that Check21 means the banks are handling digital images of checks, so most of the comparison task can be automated.
I myself write few enough checks that I buy them from the bank 3 at a time. My bank knows which numbers they issued, and they certainly know the appearance of their own checks.
Regardless, presuming "always online" is always a mistake
I see many, many proposals to enhance financial security, and they all have the same thing in common: they presume an "always online" internet connection. And I think to myself, "Wow, this person lives in a big city."
Because you get into mountain country, or even just the wrong block in suburbia or exurbia, and forget about it.
I'm sure there'd be an inter-bank clearinghouse to confirm the validity of checks online. However, without solid internet at an acceptance location, it would not be viable for check acceptors to validate the check at time of sale.
Further, checks are extremely well-established in the law
The evidence chain is simple. There you are, holding the bounced check in your hand. Your local bank manager will attest to its being refused, and is ready to explain the complexities of the check clearinghouse system to a jury. Courts like paper. They especially like paper when it has longstanding conventions as to its meaning, to which many readily available neutral parties can attest.
In Check21 this may be paper that has been reprinted from a scan of original documents, but again, any bank manager will swear to the veracity of that system. And the check system has been tuned for centuries to make it easily defended in court.
That quells arguments about the paper's meaning and validity.
The evidence is clear enough that it wasn't hard to criminalize misdeeds with paper checks. The criminal justice system is pretty good at sending fraudsters to jail on check-fraud charges alone. This serves as a potent deterrent to check fraud; at least local check fraud.
Note that in the instant case (the one you link), the miscreant got caught. Easily.