You're being downvoted for some reason, but you are right. This is a variation of the Gambler's fallacy, where the miner thinks that because it has mined on branch 0 for some time, the expected time to mine a block on branch 0 in the future will be shorter than on branch 0'.
By way of directly illustrating this, consider slot machines with identical payouts. Grandma has been inserting coins into slot machine A for twenty minutes, when suddenly slot machine A' is turned on. There's no difference between continuing to pump coins into slot machine A and switching slot machine A', the expected payoff is the same either way.
The argument depends crucially on how the hash space is searched. If you could avoid inputs that yield previously seen hash outputs then it would be the case that time previously spent mining would decrease the expected time until getting a valid hash. That doesn't happen by design.
Analogies to slot machines and flipping coins obscures this fact.
How would one productively store previously seen hash outputs? The problem is multi-fold:
Storing the minimum target nonce seen during mining has a key-space of size 256+96=352bits { midstate + { merkle_root, ntime, nbits } }.
So 1/2^352 chance of ever having a collision. Or 2.725094297605216460742E-107. 107 zeros between the decimal and the first interesting digit.
However you wouldn't have indexed this because ntime (the current time) is always going to be unique, and nbits (the current difficulty) might as well be too.
A single bit change in any part of the key completely changes the result, so there is no pattern you can infer by only storing a prefix.
Such a strategy is doomed.
EDIT: ntime is effectively unique as it is the Unix time and will roll over after many years, but the Bitcoin network requires mined blocks to have an ntime within threshold of the current actual time.
This is mostly true. Sometimes it's worth it to continue playing on the original slot machine if it has some sort of progressive feature like a jackpot that isn't shared with other machines of the same type.
By way of directly illustrating this, consider slot machines with identical payouts. Grandma has been inserting coins into slot machine A for twenty minutes, when suddenly slot machine A' is turned on. There's no difference between continuing to pump coins into slot machine A and switching slot machine A', the expected payoff is the same either way.