The issue with this is that it doesn't validate as a reasonable approach, neither a logical one.

This is why. Since you agree with the laws of the uniform distribution, then some logical conclusions immediately follow from them:

Theorem: the probability of any range is exactly identical to the probability of any set of keys you can think of, of the same length.

Hence, it is exactly the same thing whether you scan a range, or scan a set, or wait it out 10 minutes and continue from some other key, or if you jump around, or if you give up and ask a friend to continue scanning on his computer. All of these events have the same amount of extra success, because they're all independent.

BUT - scanning sequentially is the fastest and most efficient way that this can practically be done. Why? Because:

1. It's a bitch to keep track of what was randomly scanned - inefficiency, resource wasting, time consuming, avoiding birthday paradox, needing some sort of database.
2. Starting off a job from some X index, requires computing the public key from the private key - inefficiency, resource consumption, more processing time.
3. It's simply the most efficient and easy to scale method.

Now, since the probabilities are exactly identical in all cases, where is the logic and reasonability of  complicating things?

You are spreading this fake sentiment that playing the lottery with the puzzle increases chances. It does not.

If one scans keys 5327542 and 3528294356, the chances of finding the key are identical as if they simply scanned the first and second keys of the puzzle. Or the last two. Or the middle two. Or keys 42 and 99999. This is probably what doesn't make sense to you, unfortunately.

So, scanning some range in sequence, has the exact same probability of success as if you randomly pick up any other keys, check if they were scanned or not, compute their pubKey from scratch, and then check them.

Which of the two options is the most logical and reasonable?