I understand what you're saying about "execution" being more important than the idea - that is true, but execution also means follow through. Building an MVP and then ditching it to pursue "the next project" is not execution, that's just pure labor, which anyone can find for far cheaper on elance.
Second, if the business is promising and I have a significant equity in it, of course I'll pour more work into it. I'm on the next project only while the other party does their part marketing until we evaluate in a couple months if it's working out.
And I also want to point out that my work is not something you can buy on elance at all, and most definitely not for cheap anywhere.
In your proposition, the main incentive is your coding ability.
The key difference is that in the first scenario, the cash is a measurable benefit. In your scenario, your coding ability is uncertain, it could be worth more or less than the cash you are requesting - it's hardly worth gambling 50% equity on ones self-proclaimed ability.