However, as soon as you mine (or buy) Bitcoin, and if you decide to hold them, you are now incentive-aligned with all other Bitcoin holders in desiring a future where Bitcoin is more valuable.
That's much like the incentive-alignment of founding (and early-investor) equity in a startup venture. You know what your share is, and want it to be worth more. So even separate from any salaries or formal-obligations, you can be expected to improvise to help collaboratively create the world where your shares are more valuable.
Other equity is similar: it's a claim on a certain package of legally-respected rights. (You can vote in board elections; you can collect dividends; you receive pro-rata value in case of liquidation.) Those rights might be worth a lot, in certain possible futures, or nothing, in others. If you're an employee-stockholder, you may be a bit more motivated that someone on a fixed salary. If you're an outside shareholder, you'll still "talk your book" and perhaps even direct other investments in ways that synergistically boost the startup.
People describe Bitcoin as crypto-currency or crypto-commodity, but its biggest impact may be as crypto-equity.