There is a theory that replay protection applied in a split chain increases the relative utility of the original chain. Replay protection is a rule designed relative to another chain and with a directional behavior. The protection makes transactions of the protected chain invalid on the other.

Even without protection it is possible for an owner to spend in a manner that prevents replay in one direction or the other, though there is a fee and/or complexity cost in doing so. A split may reduce, but not eliminate, this cost in one or both directions by activating rules that spends can selectively utilize. This is called opt-in, in contrast to mandatory, replay protection. Opt-in replay protection reduces but does not eliminate the cost whereas mandatory protection can eliminate the cost.

The replay of a spend onto another chain is non-dilutive. The common output can be spent on either chain with or without replay. The only distinction provided by protection is that spends can always be distinct on each chain with no extra cost to the spender. The supply in each chain remains unaffected by protection.

It is a curious misperception that one chain can somehow absorb the transactions of another in a split. All outputs of the common segment remain spendable on both chains. Replay protection only reduces the cost of spending them on the protected chain.

One might assume that the lack of protection makes an owner less likely to spend on the unprotected chain, thereby limiting supply and increasing exchange price. However this assumes demand is unaffected by what amounts to an increase in trading cost. If the owner is not trading because of an increased cost in doing so, then the utility of the coin is not increased but decreased.

The self-protection cost amounts to a one-time demurrage that persists until protection is applied to unprotected units, intentionally or otherwise. This cost is a discount to the utility of an unprotected chain in relation to the hypothetical same chain with protection. This implies greater utility of a protected chain relative to the unprotected chain against which it is split than would otherwise be the case. Therefore the theory is invalid.