I think this is the intuitive way to think about specialness in bond futures, at least to my mind; therefore, I am wondering if my logic is correct:
Cash Bonds have a forward price that is totally deterministic today based on its carry, which is income - financing + any pull to par. This is the actual no-arbitrage future price of the security.
The futures give you an estimated futures price, and therefore an estimate of carry, which is influenced by many things, like demand/supply/deliverable switching. If the implied carry is higher in the futures market than the underlying bond, meaning the forward price of the bond according to the futures is cheaper, there is some specialness in the futures, and there is extra carry in the futures.
How is the specialness realized in a long only cash portfolio? Because spot and futures prices must converge, the futures price will move toward that no-arb actual forward price as the contract gets closer to maturity, and that specialness is realized. Of course, being exposed to the duration will make changes in rates dominate total return, but that specialness will provide for something of a cushion if the trade goes against you.
If the forward curve is realized, the futures will simply converge to the actual forward price, and the position will earn the specialness.
Is this correct?